OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 7 — Mar. 26, 2012
  • pp: 7792–7806
« Show journal navigation

Decelerating a pulsed subsonic molecular beam by a quasi-cw traveling optical lattice

Xiang Ji, Qi Zhou, Zhenxing Gu, and Jianping Yin  »View Author Affiliations


Optics Express, Vol. 20, Issue 7, pp. 7792-7806 (2012)
http://dx.doi.org/10.1364/OE.20.007792


View Full Text Article

Acrobat PDF (2728 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We propose a promising scheme to realize the deceleration of a pulsed subsonic molecular beam by using a multistage optical Stark decelerator (i.e., a 1D quasi-cw traveling optical lattice), which is composed of two nearly counter-propagating, time-varying, red-detuned light fields with an intensity of ~107Wcm−2 and a fixed frequency difference between them. We also study the influence of the velocity reduced amount of the traveling lattice, the lattice power, the synchronous phase angle, the deceleration-stage number and the temporal profile of laser pulses on the molecular slowing results by using 3D Monte-Carlo method. Our study shows that the proposed decelerator cannot only be used to slow a pulsed subsonic beam from 240m/s to standstill, but also to obtain a cold molecular packet with a temperature of a few µK, and the corresponding fraction of cold molecules is 10−6-10−7, which strongly depends on the synchronous phase angle. And we also find that a pair of appropriate rising and falling times of laser pulses will lead to a better slowing effect than that produced by the top-hat temporal ones.

© 2012 OSA

1. Introduction

In recent years, many promising approaches have been developed for obtaining cold or ultracold neutral molecules, such as photoassociation [1

1. U. Schlöder, C. Silber, and C. Zimmermann, “Photoassociation of heteronuclear lithium,” Appl. Phys. B 73(8), 801–805 (2001). [CrossRef]

] and Feshbach resonances [2

2. C. A. Regal, C. Ticknor, J. L. Bohn, and D. S. Jin, “Creation of ultracold molecules from a Fermi gas of atoms,” Nature 424(6944), 47–50 (2003). [CrossRef] [PubMed]

] for laser-cooled atoms, buffer gas cooling [3

3. D. C. Weinstein, J. Marden, F. Carnevali, and A. Hemmati-Brivanlou, “Magnetic trapping of calcium monohydride molecules at millikelvin temperatures,” Nature 395(6705), 148–150 (1998). [CrossRef]

], electrostatic Stark decelerator for polar molecules [4

4. M. R. Tarbutt, H. L. Bethlem, J. J. Hudson, V. L. Ryabov, V. A. Ryzhov, B. E. Sauer, G. Meijer, and E. A. Hinds, “Slowing heavy, ground-state molecules using an alternating gradient decelerator,” Phys. Rev. Lett. 92(17), 173002 (2004). [CrossRef] [PubMed]

], a magnetic Zeeman slower for paramagnetic molecules [5

5. N. Vanhaecke, U. Meier, M. Andrist, B. H. Meier, and F. Merkt, “Multistage Zeeman deceleration of hydrogen atoms,” Phys. Rev. A 75(3), 031402 (2007). [CrossRef]

], and optical Stark decelerator for all kinds of neutral molecules [6

6. R. Fulton, A. I. Bishop, M. N. Shneider, and P. F. Barker, “Controlling the motion of cold molecules with deep periodic optical potentials,” Nat. Phys. 2(7), 465–468 (2006). [CrossRef]

], low-pass velocity filter [7

7. Y. Liu, M. Yun, Y. Xia, L. Deng, and J. Yin, “Experimental generation of a cw cold CH3CN molecular beam by a low-pass energy filtering,” Phys. Chem. Chem. Phys. 12(3), 745–752 (2009). [CrossRef] [PubMed]

9

9. R. Liu, Q. Zhou, Y. Yin, and J. Yin, “Laser guiding of cold molecules in a hollow photonic bandgap fiber,” J. Opt. Soc. Am. B 26(5), 1076–1083 (2009). [CrossRef]

], laser cooling [10

10. E. S. Shuman, J. F. Barry, and D. Demille, “Laser cooling of a diatomic molecule,” Nature 467(7317), 820–823 (2010). [CrossRef] [PubMed]

] and so on. Recently, a single-stage (or multistage) optical Stark decelerator using a far-off-resonance, red-detuned, moving (or static), pulsed (or quasi-cw) optical lattice has attracted much attention of people [6

6. R. Fulton, A. I. Bishop, M. N. Shneider, and P. F. Barker, “Controlling the motion of cold molecules with deep periodic optical potentials,” Nat. Phys. 2(7), 465–468 (2006). [CrossRef]

, 11

11. P. F. Barker and M. N. Shneider, “Optical microlinear accelerator for molecules and atoms,” Phys. Rev. A 64(3), 033408 (2001). [CrossRef]

15

15. Y. Yin, Q. Zhou, L. Deng, Y. Xia, and J. Yin, “Multistage optical Stark decelerator for a pulsed supersonic beam with a quasi-cw optical lattice,” Opt. Express 17(13), 10706–10717 (2009). [CrossRef] [PubMed]

]. In 2001 and 2002, Barker’s group put forward a traveling periodic dipole potential of an optical lattice created by high-intensity short-pulse lasers to accelerate and decelerate atoms or molecules [11

11. P. F. Barker and M. N. Shneider, “Optical microlinear accelerator for molecules and atoms,” Phys. Rev. A 64(3), 033408 (2001). [CrossRef]

, 12

12. P. F. Barker and M. N. Shneider, “Slowing molecules by optical microlinear deceleration,” Phys. Rev. A 66(6), 065402 (2002). [CrossRef]

]. In 2006, they also proposed and realized an effectively slowing of a supersonic NO molecular beam by using a traveling pulse optical lattice with a well-depth of 22K (i.e., a single-stage optical Stark decelerator) [6

6. R. Fulton, A. I. Bishop, M. N. Shneider, and P. F. Barker, “Controlling the motion of cold molecules with deep periodic optical potentials,” Nat. Phys. 2(7), 465–468 (2006). [CrossRef]

], and J. Ramirez-Serrano, et al experimentally demonstrated a similar single-stage optical Stark deceleration for a supersonic H2 molecular beam with a static pulse optical lattice [13

13. J. Ramirez-Serrano, K. E. Strecker, and D. W. Chandler, “Modification of the velocity distribution of H2 molecules in a supersonic beam by intense pulsed optical gradients,” Phys. Chem. Chem. Phys. 8(25), 2985–2989 (2006). [CrossRef] [PubMed]

]. In 2009, Momose’s group proposed a multistage optical Stark decelerator scheme for a pre-cooling pulsed molecular beam with an initial velocity of 13-15m/s and a temperature of 100-500mK by using a quasi-cw, near-resonant and cavity-enhanced IR optical lattice [14

14. S. Kuma and T. Momose, “Deceleration of molecules by dipole force potential: a numerical simulation,” New J. Phys. 11(5), 055023 (2009). [CrossRef]

]. Also, our group proposed a useful multistage optical Stark decelerator for a supersonic (or subsonic) molecular beam with an initial velocity of 240-400m/s by using a far-off-resonance, red-detuned, quasi-cw optical lattice with a waist of 20µm and a power of 264W in 2009, and studied its deceleration effects for a subsonic CH4 beam and a supersonic NO beam by using 1D Monte-Carlo simulations [15

15. Y. Yin, Q. Zhou, L. Deng, Y. Xia, and J. Yin, “Multistage optical Stark decelerator for a pulsed supersonic beam with a quasi-cw optical lattice,” Opt. Express 17(13), 10706–10717 (2009). [CrossRef] [PubMed]

]. But there are three problems in this scheme [15

15. Y. Yin, Q. Zhou, L. Deng, Y. Xia, and J. Yin, “Multistage optical Stark decelerator for a pulsed supersonic beam with a quasi-cw optical lattice,” Opt. Express 17(13), 10706–10717 (2009). [CrossRef] [PubMed]

]: (1) The laser waist (20µm) is too small to obtain a longer lattice and more cold molecules; (2) We didn’t consider the transverse molecular loss in our 1D simulations; (3) It needs a longer optical lattice in order to slow molecular velocity to zero because the relative velocity between the initial velocity (240-400m/s) of supersonic (or subsonic) molecular beam and a static optical lattice is too large. To solve these problems, in this paper, we propose a more desirable multistage optical Stark decelerator for a subsonic (or supersonic) molecular beam by using a far-off-resonance, red-detuned, quasi-cw, traveling optical lattice with a diameter of 100µm and an intensity of ~107Wcm−2, and study its slowing results by 3D Monte-Carlo simulations. In our scheme, a shorter lattice and a shallower optical potential are only needed compared with the static lattice [15

15. Y. Yin, Q. Zhou, L. Deng, Y. Xia, and J. Yin, “Multistage optical Stark decelerator for a pulsed supersonic beam with a quasi-cw optical lattice,” Opt. Express 17(13), 10706–10717 (2009). [CrossRef] [PubMed]

]. This paper is organized as follows: In section 2, our proposed new slowing scheme and its principle for molecules are briefly introduced. In section 3, the slowing effects (including the final most-probable velocity, the fraction of cold CH4 molecules and its temperature) of our moving optical lattice with different synchronous phase angles are studied. Also, the dependences of the deceleration-stage numbers on the velocity reduced amount of the moving lattice, lattice power, and synchronous phase angle are investigated. In section 4, we study the influence of temporal shape of laser pulses on the slowing results. In section 5, we compare the slowing results of this moving lattice with the static one using the same parameters to show some advantages of our slowing scheme and also compare the slowing results of our scheme with the chirped optical lattice [12

12. P. F. Barker and M. N. Shneider, “Slowing molecules by optical microlinear deceleration,” Phys. Rev. A 66(6), 065402 (2002). [CrossRef]

] by 1D Monte-Carlo simulations. Some main results and conclusions are summarized in the final section.

2. Slowing scheme and its principle

The schematic diagram of our multistage optical Stark decelerator for a pulsed subsonic (or supersonic) molecular beam is indicated in Fig. 1(a)
Fig. 1 (a) Schematic diagram of a multistage optical Stark decelerator using a quasi-cw traveling optical lattice, which is created by two nearly counter-propagating, far-off-resonance, red-detuned laser beams with a fixed frequency difference between them, and the lattice moves along the z axis. A pulsed subsonic molecular beam propagates along the z axis and enters the quasi-cw moving lattice. The inset figure is the enlarged optical lattice. (b) The time-sequence control of moving lattice velocity for vm0 = 240m/s, ϕ0 = 90° and 120°.
. In our scheme, the multistage decelerator is composed of a red-detuned, quasi-cw moving optical lattice with a diameter of 100µm (i.e., a waist of w0 = 50µm), which is created by two nearly counter-propagating, far-off-resonance, single-frequency, linear-polarized infrared lasers with an equal intensity of I0 = 1.02 × 107Wcm−2 and a wavelength of λ = 1064nm. In Fig. 1(a), β is an angle between the two laser beams [16

16. R. Fulton, A. I. Bishop, M. N. Shneider, and P. F. Barker, “Optical Stark deceleration of nitric oxide and benzene molecules using optical lattices,” J. Phys. At. Mol. Opt. Phys. 39(19), S1097–S1109 (2006). [CrossRef]

], and both the pulsed molecular beam and the moving optical lattice are traveled along the z axis. The velocity of the moving lattice is given by vlatt = (ω1-ω2)/|k1k2|, where k1 and k2 are the wave vectors of the two counter-propagating fields, and ω1 and ω2 are their laser frequencies.

If the moving lattice is far red-detuned for the molecular resonant frequency, the optical lattice potential for molecules is given by [17

17. T. Takekoshi, J. R. Yeh, and R. J. Knize, “Quasi-electrostatic trap for neutral atoms,” Opt. Commun. 114(5-6), 421–424 (1995). [CrossRef]

]
U(z,t)=12αE(z,t)2
(1)
where α is the effective polarizability of the molecule, E(z, t) is the electric field strength of the optical lattice, and the interference term between light fields can be expressed as [18

18. M. N. Shneider, P. F. Barker, and S. F. Gimelshein, “Molecular transport in pulsed optical lattices,” Appl. Phys., A Mater. Sci. Process. 89(2), 337–350 (2007). [CrossRef]

]
E(z,t)2=E1(t)E2(t)cos(qzqvlatt0tδt2)
(2)
where E1(t) and E2(t) are the amplitudes of the infrared lattice beam 1 and 2 respectively, q = |k1k2|, δ = d(ω1-ω2)/dt is the frequency chirp, and vlatt0 is the initial lattice velocity. In our scheme, the velocity of the moving lattice is a constant (i.e., the frequency difference (Δω = ω1-ω2) of the two laser beams is also a constant), so we have δ = 0.

When molecules enter a moving optical lattice along the z axis, they will experience an optical dipole interaction potential in the red-detuned optical lattice field as follows [6

6. R. Fulton, A. I. Bishop, M. N. Shneider, and P. F. Barker, “Controlling the motion of cold molecules with deep periodic optical potentials,” Nat. Phys. 2(7), 465–468 (2006). [CrossRef]

]:
U(z,t)=2αε0cI1I2cos2[12(kzΔωt)]
(3)
where I1 = I2 = I0exp[-2(x2 + y2)/w02] is the intensity of each light field, w0 is the waist (i.e., the half-width at 1/e2 maximum intensity) of the laser beams, ε0 is the permittivity in free space, c is the speed of light in vacuum, and k = (4πsin(β/2))/λ is the lattice wave-number. For CH4 molecule, we have α = 2.9 × 10−40Cm2/V.

According to Eq. (3), molecules in the red-detuned lattice will experience an optical dipole force in both the longitudinal and transverse directions. In the transverse (i.e., radial) direction, some cold and slow molecules will be confined by the oscillation motions, other molecules with a kinetic energy of larger than the transverse lattice potential will escape from the lattice. Because the optical lattice field has a constant velocity vlatt in the longitudinal direction (i.e., the z axis), it is useful to consider the motion of molecules in a reference frame of the moving lattice. In the relative reference frame, if molecules enter the optical lattice from its antinode in the longitudinal direction, they will undergo a dipole force, which is anti-parallel to their motion direction, and then gain an optical Stark energy due to ac Stark effect. The gain in potential energy will be compensated by a loss in the molecular kinetic energy due to the law of energy conservation. During this single-stage decelerating process, the slowed molecules will lose their kinetic energy, which is equal to the corresponding lattice potential energy.

In the relative reference frame, the relative longitudinal position (zr) of the slowed molecules in the traveling optical lattice is defined as a synchronous phase angle ϕ, where ϕ = zr/Λ × 360° and Λ is the spatial period of moving lattice. The point of zr = 0 (i.e., ϕ = 0°) is set at the antinode of the lattice (i.e., the maximum of the light intensity) due to its red-detuned. It is clear from Eq. (3) that the region of 00<ϕ<180° (the rear half of each lattice cell) is the decelerating phase-angle region for molecules in the red-detuned lattice, while the region of −180°<ϕ<0° is the accelerating one.

When a synchronized molecule reaches the antinode (ϕ = 0°) of the lattice, the lattice light field should be switched on in time. As soon as it arrives at the position of ϕ = ϕ0 (where ϕ0 is the synchronous phase angle of the synchronized molecule, usually we choose 0°<ϕ0≤180°), the lattice should be switched off rapidly, and then in the region of 0°<ϕϕ0, the synchronized molecules will be slowed effectively. For the red-detuned optical lattice, if this slowing process can be repeated continuously for m times, the subsonic molecular beam will be efficiently slowed to standstill. In the deceleration process, when the relative velocity of the synchronized molecule is slowed to zero, the velocity of the reference frame (i.e., the velocity of the moving lattice vlatt) should be reduced to another constant (until it reaches zero) by modulating Δω, as shown in Fig. 1(b), and the velocity reduced amount of the lattice is denoted as Δvlatt. In this paper, the initial velocity of the moving lattice is set as vlatt0 = vm0vlatt for each Δvlatt, here vm0 is the initial central velocity (240m/s) of incident molecular beam in our simulations. If Δvlatt is equal to 80m/s [see Fig. 1(b)], we will have vlatt0 = 160m/s. In the deceleration process, for ϕ0 = 90°, when the deceleration time t arrives at 101μs and later 204μs (i.e., as the relative velocity of the synchronized molecule is slowed to zero), the lattice velocity vlatt should be reduced to 80m/s and then to 0m/s. Also, for ϕ0 = 120°, vlatt should be reduced to 80m/s and then to 0m/s when t = 67μs and 137μs.

In order to form a multistage optical Stark decelerator, we also need a time-varying lattice field (so-called a quasi-cw optical lattice) to realize an efficient deceleration for a subsonic (or supersonic) molecular beam by using a strict time-sequence synchronous and control system and an electro-optic modulator (EOM).

3. Results of 3D Monte-Carlo simulation

The slowing effect of our multistage optical Stark decelerator using a traveling optical lattice is demonstrated by 3D Monte-Carlo simulations, and 1D molecular slowing in the longitudinal direction and 2D trapping in the transverse one are studied. In our simulations, the pulsed subsonic methane (CH4) molecular beam with an initial central velocity of 240m/s and a longitudinal temperature of 0.5K is used and traveled along the z axis, as shown in Fig. 1(a). We assume that the transverse and longitudinal spatial distributions of incident pulsed molecular beam are Gaussian ones, and their spatial sizes are 0.1mm and 5mm, respectively. Also, the transverse and longitudinal velocity distributions of incident pulsed molecular beam are Gaussian ones, and their velocity half widths are 2.3m/s and 40m/s, respectively. Two nearly counter-propagating, far-off-resonance, single-frequency, linear-polarized, frequency tunable ytterbium-doped fiber lasers with a power of 400W and a wavelength of 1064nm [19

19. Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single frequency ytterbium-doped fiber master oscillator power amplifier sources up to 500W,” IEEE J. Sel. Top. Quantum Electron. 13(3), 546–551 (2007). [CrossRef]

], as input laser beams with a waist of w0 = 50μm, are used to create our moving optical-lattice decelerator. A frequency difference of 944MHz or 1890MHz between two input lasers gives rise to a lattice velocity of approximately 80m/s or 160m/s, respectively. The longitudinal velocity distributions [20

20. D. C. Clary, “A theory for the photodissociation of polyatomic molecules, with application to CF3I,” J. Chem. Phys. 84(8), 4288–4298 (1986). [CrossRef]

] of the slowed molecules are detected by a micro-channel plate (MCP), which is placed at the position of about 20cm away from the start point of the lattice on the z axis.

When the deceleration stage number is m = 23122, the synchronous phase angle is ϕ0 = 90°, the velocity reduced amount of the traveling lattice is Δvlatt = 80m/s, and the initial lattice velocity is vlatt0 = 160m/s (i.e., vlatt0 = 240m/s-Δvlatt), we first study the slowing results of our moving optical lattice by 3D Monte-Carlo method, and the simulated results are shown in Fig. 2(a)
Fig. 2 Simulated longitudinal velocity distributions of CH4 molecules at the outlet of the decelerator for the synchronous phase angle (a) ϕ0 = 90° and (b) ϕ0 = 120°. Other simulated parameters are given in the plots and text.
. The horizontal axis Fig. 2 represents the longitudinal velocity of molecules, and the vertical one represents the relative molecular number (i.e., the ratio of the molecular number at each longitudinal velocity to the one at the initial most-probable velocity of the incident molecular beam). It is clear from Fig. 2(a) that there are three slowed packets after deceleration. Here three small peaks on the horizontal axis are pointed out by red circles because they are very small even difficult to be seen. To clearly show such small slowed packets, we enlarge their velocity distributions (see the above enlarged peaks). Among them, the slowed molecular packet 3 is the slowest packet with a central velocity of ~0m/s, which is our hoped result to be obtained eventually, and its final central velocity, temperature, and fraction of cold molecules are vl = 0.9m/s, Tl = 11.5μK, and n = 5.27 × 10−6 (n = N/N0, where N and N0 are the molecular numbers in the slowed molecular packet and the incident molecular pulse, respectively). The slowed molecular packet 1 and 2 are our obtained middle results due to two reductions of the lattice velocity during the deceleration process (i.e., the packet 1 is the first outcome when vlatt is reduced from 160m/s to 80m/s, and the packet 2 is the second outcome when vlatt is reduced from 80m/s to 0m/s), and their central velocities are vl = 160.7m/s and vl = 80.3m/s, respectively. From Fig. 2(a), we can find that the temperatures Tl and fractions n of cold molecules in the packet 1, 2 and 3 become lower one by one. Though the packet 3 seems higher than the packet 2, its half width is much narrower than one of the packet 2, which means both its Tl and n are lower than those of the packet 2. We also study the deceleration effects when ϕ0 = 120°, and obtain some similar results as ϕ0 = 90°, see Fig. 2(b). We can see from Fig. 2(b) that the moving lattice with only m = 15422 (which is far smaller than m = 23122 for the case of ϕ0 = 90°) can be used to decelerate CH4 molecular beam to ~0m/s from 240m/s when the other parameters are the same as ones used in Fig. 2(a), and the final central (most-probable) velocity, temperature of the slowed packet 3 and the fraction of cold molecules are vl = 0.925m/s, Tl = 4.2μK, and n = 6.4 × 10−7, respectively. Moreover, when m = 15422, the length of our moving optical Stark decelerator is only about 1.38cm.

Secondly, we investigate the dependences of the final central velocity of the slowed packet (i.e., the slowed packet 3 in Fig. 2) and its temperature as well as the fraction of cold molecules on the deceleration stage number m, and the simulated results are shown in Fig. 3
Fig. 3 Dependences of (a) the final central velocity, (b) fraction and (c) temperature of the slowest packet (i.e., the slowed packet 3 in Fig. 2) on the deceleration stage number m. Other simulated parameters are given in the plots and text.
. Figure 3(a) shows the relationship between the molecular velocity vm and the stage number m when the initial velocity of the traveling lattice is vlatt0 = 160m/s and its velocity reduced amount is Δvlatt = 80m/s, the solid lines are the fitted curves. Figure 3(b) shows the relationship between the fraction n of cold molecules in the slowed packet and the stage number m. It can be found from Fig. 3(b) that with the increase of m, the fraction n of cold molecules will be decreased gradually, and the larger the synchronous phase angle ϕ0 is, the smaller the fraction of cold molecules will be. This is because the larger the synchronous phase angle is, the smaller the area of the phase stability space is, and then the less the cold molecular number in the slowed packet is [21

21. J. R. Bochinski, E. R. Hudson, H. J. Lewandowski, G. Meijer, and J. Ye, “Phase space manipulation of cold free radical OH molecules,” Phys. Rev. Lett. 91(24), 243001 (2003). [CrossRef] [PubMed]

]. Figure 3(c) shows that with the increase of m, the temperature Tl of the slowed molecular packet will be reduced gradually, and the larger the synchronous phase angle ϕ0 is, the lower the temperature Tl of the slowed molecular packet is. This is because the number of cold molecules in the slowed packet is proportional to the area of the phase stability space. That is, the larger the synchronous phase angle is, the less the cold molecular number in the slowed packet is, and then the cooler the temperature of the slowed packet is, which is similar to the results in the evaporative cooling due to the bunching effect.

Also, it is obvious from Fig. 3 that it needs much fewer deceleration stages for slowing molecules from 240m/s to ~0m/s with ϕ0 = 120° than that with ϕ0 = 90°, and the slowed effects (vl, n and Tl) with ϕ0 = 120° are greatly better than that with ϕ0 = 90°.

In final, we study the dependences of the deceleration stage number m that need to slow a subsonic CH4 molecular beam from 240m/s to zero (i.e., to obtain the slowest packet) on the velocity reduced amount Δvlatt of the traveling lattice, the synchronous phase angle ϕ0 and the input power P0 of lattice beams, and the simulated results are shown in Fig. 4
Fig. 4 Dependences of the deceleration stage number m that needs to slow a subsonic CH4 molecular beam to zero on (a) the velocity reduced amount Δvlatt of the traveling lattice, (b) the synchronous phase angle ϕ0, and (c) the input power P0 of lattice beams. Other simulated parameters are given in the plots and text.
. We can see from Fig. 4(a) that with the increase of Δvlatt, the needed deceleration-stage number m will be increased gradually when P0 = 400W, and the larger the synchronous phase angle is, the less the needed deceleration-stage number m will be. Also, we find that the fraction n of cold molecules in the slowest molecular packet is very low as ϕ0 = 150°. So in our simulations, ϕ0 = 90° and ϕ0 = 120° are employed to demonstrate our deceleration scheme and study its slowing results (see Figs. 2, 3, and later Fig. 5
Fig. 5 Influence of the rising and falling times of laser pulses (tr and tf) on (a) final most-probable velocity vl (where lines are fitted curves and points are simulated results), (c) fraction n of cold molecules in slowed packet and temperature Tl of it. Variation of (b) turning point of tr (and tf) with the synchronous phase angle ϕ0 and (d) optical dipole force experienced by molecules on the z axis in one spatial period of traveling lattice. Other simulated parameters are given in the plots and text.
). It can be found from Fig. 4(b) that with the increase of ϕ0, the needed deceleration-stage number m will be decreased gradually when P0 = 400W, and when the synchronous phase angle ϕ0 is given, the smaller the velocity reduced amount Δvlatt of the moving lattice is, the less the needed deceleration-stage number will be. In particular, when ϕ0 = 150° and Δvlatt = 40m/s, the needed deceleration-stage number is only m = 6500. However, we know from our simulated results that the larger the velocity reduced amount Δvlatt is, the more the obtained cold molecules in the slowest packet will be. So Δvlatt = 80m/s is used in our simulations (see Figs. 2, 3, and later Fig. 5). We can also find from Fig. 4(c) that the larger the laser power P0 is, and the smaller the velocity reduced amount Δvlatt is, the less the needed deceleration-stage number m will be.

These results show that the deceleration-stage number m that needs to slow a subsonic molecular beam from 240/s to 0m/s is not only relative to the velocity reduced amount Δvlatt of the moving lattice and its power P0, but also to the synchronous phase angle ϕ0, and when the velocity reduced amount Δvlatt is smaller, and the synchronous phase angle ϕ0 is larger, the needed deceleration-stage number m is less, but in this case, the obtainable cold molecules are less. So in order to obtain more and colder molecules, we should make a compromising consideration for Δvlatt and ϕ0.

4. Influences induced by rising and falling times of laser pulses

It can also be understood easily that the larger the synchronous phase angle ϕ0 is, the shorter the rising and falling times (tr and tf) of laser pulses contributing to the slowing of molecules will be. Thus the turning point with ϕ0 = 150° appears earlier than one with other synchronous phase angles such as ϕ0 = 120°, ϕ0 = 90° and ϕ0 = 60° on the horizontal axis. As shown in Fig. 5(b), with the increase of ϕ0, the turning point of tr and tf will be lower and lower.

Figure 5(c) shows the influence of tr and tf on the temperature Tl of the slowed packet and fraction n of cold molecules when ϕ0 = 90° and the final most-probable velocity vl of slowed molecules is below 1m/s. It is clear that with increase of tr and tf, both Tl and n decrease gradually. This is because tr and tf will result in more shallow optical potentials in the deceleration process, so that less cold molecules can be trapped and Tl of the slowed packet will also be lower.

5. Discussion

In 2009, our group proposed a multistage optical Stark decelerator using a 1D quasi-cw static optical lattice for a pulsed supersonic (or subsonic) molecular beam [15

15. Y. Yin, Q. Zhou, L. Deng, Y. Xia, and J. Yin, “Multistage optical Stark decelerator for a pulsed supersonic beam with a quasi-cw optical lattice,” Opt. Express 17(13), 10706–10717 (2009). [CrossRef] [PubMed]

], and studied its deceleration effects for a subsonic CH4 beam and a supersonic NO beam by using 1D Monte-Carlo simulations. In this section, we will compare the deceleration results of this static-lattice decelerator with that of our proposed traveling lattice one for the same subsonic CH4 beam, and the simulated results are shown in Fig. 6
Fig. 6 Simulated final central velocities of slowed CH4 molecular packets decelerated by a static or traveling optical lattice, respectively. Other simulated parameters are given in the plots and text.
. In our simulations and comparison, we use the same lattice parameters and incident pulsed subsonic CH4 beam, and for the quasi-cw traveling lattice, the velocity reduced amount of the traveling lattice is chosen as Δvlatt = 80m/s (i.e., its initial velocity is vlatt0 = 160m/s). It is clear from Fig. 6 that the velocity reduction of subsonic molecular beam produced by the traveling optical lattice is much larger than that by the static one. In particular, within the deceleration stage number of m = 0-16000, the traveling lattice can be used to slow a subsonic CH4 beam from 240m/s to about 0.9m/s, but the static one can only be used to slow the CH4 beam from 240m/s to ~195.5m/s.

That means it needs much more deceleration stages for slowing a subsonic molecular beam to standstill by using a quasi-cw static optical lattice than that by using a quasi-cw traveling one. This shows that our traveling optical lattice can be used to realize more efficient deceleration than the static one. This is because the relative velocity between the moving lattice and subsonic molecular beam in our proposed traveling-lattice decelerator is much lower than that in the static-lattice decelerator, while the interaction time of the slowed molecules with the traveling lattice is much longer. Then molecules can obtain better deceleration effects when the moving optical lattice is employed. Also, Fig. 6 shows that the traveling lattice with a length of only about 1.38cm (i.e., a deceleration stage of 16000) can be used to slow a subsonic molecular beam from 240m/s to ~0m/s, but for the static one, m = 40000 (i.e., a lattice length of about 2.13cm) is needed to slow a subsonic beam from 240m/s to ~0m/s.

In 2002, Barker’s group put forward a general scheme for creating stationary cold molecules by rapid deceleration of supersonically cooled molecules in a high-intensity pulsed optical lattice [12

12. P. F. Barker and M. N. Shneider, “Slowing molecules by optical microlinear deceleration,” Phys. Rev. A 66(6), 065402 (2002). [CrossRef]

]. Next, we will compare the efficiency of their scheme using a chirped decelerating optical lattice with our proposal using a traveling lattice with a constant velocity (i.e., the frequency chirp δ = 0) by 1D Monte-Carlo simulation, and the results are shown in Fig. 7
Fig. 7 Comparison of the deceleration effects of (a) our traveling lattice with (b) a chirped optical lattice. Other simulated parameters are shown in the plots and text.
. In the simulations, we take molecule I2 as an example and the pulsed I2 molecular beam has the same initial central velocity of 400m/s and longitudinal temperature of 1.0K. Figure 7(a) shows the results of our scheme when I0 = 6.4 × 107Wcm−2, ϕ0 = 90° and Δvlatt = 100m/s.

When the slowed packet is decelerated to a velocity of 160m/s, the corresponding temperature and the fraction n of cold molecules are Tl = 6.08μK and n = 0.15%, respectively. Figure 7(b) shows the deceleration results of a chirped optical lattice when I0 = 12 × 109Wcm−2, ψ = 0.735, δ = 5.28 × 1015rad/s and q = 1.56 × 107/m which are the same as ones used in Ref. [12

12. P. F. Barker and M. N. Shneider, “Slowing molecules by optical microlinear deceleration,” Phys. Rev. A 66(6), 065402 (2002). [CrossRef]

]. When molecules are decelerated to the same velocity 160m/s, the velocity width of the slowed packet is very broad, the corresponding Tl and n are 453.3mK and 11.49%, respectively. These show that the number of cold molecules in the chirped optical-lattice slowing scheme is almost two orders of magnitude higher than that of our slowing one, but the temperature Tl of the slowed packet in our scheme is much lower than that in the chirped optical-lattice scheme by about five orders of magnitude owing to the bunching effect of our multistage optical Stark decelerator.

6. Summary

In this paper, we have proposed and demonstrated a promising scheme to slow a pulsed subsonic molecular beam by using a far-off-resonance, red-detuned, quasi-cw traveling optical lattice with an intensity of ~107Wcm−2. By using 3D Monte-Carlo method, we have studied the slowing results (including the final central velocity vl of the slowed packet and its temperature as well as the fraction of cold molecules) of our moving optical lattice for different synchronous phase angle. We have also investigated the dependences of the deceleration-stage number m needed to slow a subsonic molecular beam from 240m/s to zero on the velocity reduced amount Δvlatt of the traveling lattice and its power as well as the synchronous phase angle ϕ0. Our study shows that a far-off-resonance, red-detuned, quasi-cw traveling optical lattice, as a multistage optical Stark decelerator with a length of only short than 1.4cm, can be used to efficiently slow a subsonic molecular beam from 240m/s to zero, and a cold molecular packet with a temperature of a few μK can be obtained, but the corresponding fraction of cold molecules will be 10−6~10−7, which strongly depends on our choosing ϕ0. This shows that when the molecular number in an incident molecular pulse is equal to 1012, our obtainable number of cold molecules in the slowed packet can reach 105~106. We have also found that the larger the synchronous phase angle ϕ0 is, the lower the final central velocity of the slowed packet is, and the less the cold molecular number is, and then the lower the temperature of cold molecules is. In addition, a larger ϕ0, a smaller Δvlatt, or a higher P0 will result in a less deceleration stage number m that needs to slow a subsonic molecular beam to zero and a shorter quasi-cw, traveling optical lattice. Besides, we have taken the time-dependent intensity of laser pulses into account and investigated its influence on the slowing effects. Our study shows that (1) with the increase of the rising time tr and the falling time tf, the final velocity vl of the slowed packet will first drop and then rise, that is, there is an optimal turning point for each synchronous phase angle. (2) The larger the synchronous phase angle is, the shorter the rising and falling times (tr and tf) of laser pulses contributing to the slowing of molecules will be. (3) A pair of appropriate tr and tf will lead to a better slowing effect than that produced by the top-hat temporal laser pulses. Moreover, we have compared the slowing results of our proposed traveling-lattice decelerator with the static-lattice one, and found that the traveling-lattice molecular decelerator is more efficient than the static-lattice one under the same slowing conditions. Finally, we have compared the slowing performances of our scheme with a chirped optical lattice proposed in Ref. [12

12. P. F. Barker and M. N. Shneider, “Slowing molecules by optical microlinear deceleration,” Phys. Rev. A 66(6), 065402 (2002). [CrossRef]

], and found that our multistage decelerator can obtain a cooler molecular packet due to the bunching effect, but a chirped lattice scheme can get more cold molecules.

Our proposed traveling optical-lattice decelerator cannot only be used to efficiently slow all kinds of neutral molecules, including polar molecules, paramagnetic molecules and those molecules without a permanent electric or magnetic dipole moment, but also to obtain an ultracold molecular packet with a temperature of 4.2μK and a number of 105~106. So such a multistage optical Stark decelerator using a traveling lattice and its obtainable ultracold molecules have some important applications in the fields of cold molecular physics, cold molecular spectrum, cold molecular collisions and cold chemistry, precise measurement, quantum computing and its information processing, and cold molecular lithography, even it can be used to realize an all-optical, chemically-stabled molecular Bose-Einstein condensates (BEC) by using an optical-potential evaporative cooling [22

22. J. Yin, “Realization and research of optically-trapped quantum degenerate gases,” Phys. Rep. 430(1-2), 1–116 (2006). [CrossRef]

], all-optical molecular Fermi quantum degeneration (FQNG), quantum and nonlinear molecule optics, and so on.

Acknowledgment

This work is supported by the National Nature Science Foundation of China under Grant Nos. 10674047, 10804031, 10904037, 10974055 and 11034002, the National Key Basic Research and Development Program of China under Grant Nos. 2006CB921604 and 2011CB921602, and the Basic Key Program of Shanghai Municipality under Grant No. 07JC14017, and the Shanghai Leading Academic Discipline Project under Grant No.B408.

References and links

1.

U. Schlöder, C. Silber, and C. Zimmermann, “Photoassociation of heteronuclear lithium,” Appl. Phys. B 73(8), 801–805 (2001). [CrossRef]

2.

C. A. Regal, C. Ticknor, J. L. Bohn, and D. S. Jin, “Creation of ultracold molecules from a Fermi gas of atoms,” Nature 424(6944), 47–50 (2003). [CrossRef] [PubMed]

3.

D. C. Weinstein, J. Marden, F. Carnevali, and A. Hemmati-Brivanlou, “Magnetic trapping of calcium monohydride molecules at millikelvin temperatures,” Nature 395(6705), 148–150 (1998). [CrossRef]

4.

M. R. Tarbutt, H. L. Bethlem, J. J. Hudson, V. L. Ryabov, V. A. Ryzhov, B. E. Sauer, G. Meijer, and E. A. Hinds, “Slowing heavy, ground-state molecules using an alternating gradient decelerator,” Phys. Rev. Lett. 92(17), 173002 (2004). [CrossRef] [PubMed]

5.

N. Vanhaecke, U. Meier, M. Andrist, B. H. Meier, and F. Merkt, “Multistage Zeeman deceleration of hydrogen atoms,” Phys. Rev. A 75(3), 031402 (2007). [CrossRef]

6.

R. Fulton, A. I. Bishop, M. N. Shneider, and P. F. Barker, “Controlling the motion of cold molecules with deep periodic optical potentials,” Nat. Phys. 2(7), 465–468 (2006). [CrossRef]

7.

Y. Liu, M. Yun, Y. Xia, L. Deng, and J. Yin, “Experimental generation of a cw cold CH3CN molecular beam by a low-pass energy filtering,” Phys. Chem. Chem. Phys. 12(3), 745–752 (2009). [CrossRef] [PubMed]

8.

B. Ghaffari, J. M. Gerton, W. I. McAlexander, K. E. Strecker, D. M. Homan, and R. G. Hulet, “Laser-free slow atom source,” Phys. Rev. A 60(5), 3878–3881 (1999). [CrossRef]

9.

R. Liu, Q. Zhou, Y. Yin, and J. Yin, “Laser guiding of cold molecules in a hollow photonic bandgap fiber,” J. Opt. Soc. Am. B 26(5), 1076–1083 (2009). [CrossRef]

10.

E. S. Shuman, J. F. Barry, and D. Demille, “Laser cooling of a diatomic molecule,” Nature 467(7317), 820–823 (2010). [CrossRef] [PubMed]

11.

P. F. Barker and M. N. Shneider, “Optical microlinear accelerator for molecules and atoms,” Phys. Rev. A 64(3), 033408 (2001). [CrossRef]

12.

P. F. Barker and M. N. Shneider, “Slowing molecules by optical microlinear deceleration,” Phys. Rev. A 66(6), 065402 (2002). [CrossRef]

13.

J. Ramirez-Serrano, K. E. Strecker, and D. W. Chandler, “Modification of the velocity distribution of H2 molecules in a supersonic beam by intense pulsed optical gradients,” Phys. Chem. Chem. Phys. 8(25), 2985–2989 (2006). [CrossRef] [PubMed]

14.

S. Kuma and T. Momose, “Deceleration of molecules by dipole force potential: a numerical simulation,” New J. Phys. 11(5), 055023 (2009). [CrossRef]

15.

Y. Yin, Q. Zhou, L. Deng, Y. Xia, and J. Yin, “Multistage optical Stark decelerator for a pulsed supersonic beam with a quasi-cw optical lattice,” Opt. Express 17(13), 10706–10717 (2009). [CrossRef] [PubMed]

16.

R. Fulton, A. I. Bishop, M. N. Shneider, and P. F. Barker, “Optical Stark deceleration of nitric oxide and benzene molecules using optical lattices,” J. Phys. At. Mol. Opt. Phys. 39(19), S1097–S1109 (2006). [CrossRef]

17.

T. Takekoshi, J. R. Yeh, and R. J. Knize, “Quasi-electrostatic trap for neutral atoms,” Opt. Commun. 114(5-6), 421–424 (1995). [CrossRef]

18.

M. N. Shneider, P. F. Barker, and S. F. Gimelshein, “Molecular transport in pulsed optical lattices,” Appl. Phys., A Mater. Sci. Process. 89(2), 337–350 (2007). [CrossRef]

19.

Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single frequency ytterbium-doped fiber master oscillator power amplifier sources up to 500W,” IEEE J. Sel. Top. Quantum Electron. 13(3), 546–551 (2007). [CrossRef]

20.

D. C. Clary, “A theory for the photodissociation of polyatomic molecules, with application to CF3I,” J. Chem. Phys. 84(8), 4288–4298 (1986). [CrossRef]

21.

J. R. Bochinski, E. R. Hudson, H. J. Lewandowski, G. Meijer, and J. Ye, “Phase space manipulation of cold free radical OH molecules,” Phys. Rev. Lett. 91(24), 243001 (2003). [CrossRef] [PubMed]

22.

J. Yin, “Realization and research of optically-trapped quantum degenerate gases,” Phys. Rep. 430(1-2), 1–116 (2006). [CrossRef]

OCIS Codes
(020.0020) Atomic and molecular physics : Atomic and molecular physics
(020.6580) Atomic and molecular physics : Stark effect
(020.7010) Atomic and molecular physics : Laser trapping
(020.3320) Atomic and molecular physics : Laser cooling

ToC Category:
Atomic and Molecular Physics

History
Original Manuscript: December 20, 2011
Revised Manuscript: March 8, 2012
Manuscript Accepted: March 16, 2012
Published: March 21, 2012

Citation
Xiang Ji, Qi Zhou, Zhenxing Gu, and Jianping Yin, "Decelerating a pulsed subsonic molecular beam by a quasi-cw traveling optical lattice," Opt. Express 20, 7792-7806 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-7-7792


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. U. Schlöder, C. Silber, C. Zimmermann, “Photoassociation of heteronuclear lithium,” Appl. Phys. B 73(8), 801–805 (2001). [CrossRef]
  2. C. A. Regal, C. Ticknor, J. L. Bohn, D. S. Jin, “Creation of ultracold molecules from a Fermi gas of atoms,” Nature 424(6944), 47–50 (2003). [CrossRef] [PubMed]
  3. D. C. Weinstein, J. Marden, F. Carnevali, A. Hemmati-Brivanlou, “Magnetic trapping of calcium monohydride molecules at millikelvin temperatures,” Nature 395(6705), 148–150 (1998). [CrossRef]
  4. M. R. Tarbutt, H. L. Bethlem, J. J. Hudson, V. L. Ryabov, V. A. Ryzhov, B. E. Sauer, G. Meijer, E. A. Hinds, “Slowing heavy, ground-state molecules using an alternating gradient decelerator,” Phys. Rev. Lett. 92(17), 173002 (2004). [CrossRef] [PubMed]
  5. N. Vanhaecke, U. Meier, M. Andrist, B. H. Meier, F. Merkt, “Multistage Zeeman deceleration of hydrogen atoms,” Phys. Rev. A 75(3), 031402 (2007). [CrossRef]
  6. R. Fulton, A. I. Bishop, M. N. Shneider, P. F. Barker, “Controlling the motion of cold molecules with deep periodic optical potentials,” Nat. Phys. 2(7), 465–468 (2006). [CrossRef]
  7. Y. Liu, M. Yun, Y. Xia, L. Deng, J. Yin, “Experimental generation of a cw cold CH3CN molecular beam by a low-pass energy filtering,” Phys. Chem. Chem. Phys. 12(3), 745–752 (2009). [CrossRef] [PubMed]
  8. B. Ghaffari, J. M. Gerton, W. I. McAlexander, K. E. Strecker, D. M. Homan, R. G. Hulet, “Laser-free slow atom source,” Phys. Rev. A 60(5), 3878–3881 (1999). [CrossRef]
  9. R. Liu, Q. Zhou, Y. Yin, J. Yin, “Laser guiding of cold molecules in a hollow photonic bandgap fiber,” J. Opt. Soc. Am. B 26(5), 1076–1083 (2009). [CrossRef]
  10. E. S. Shuman, J. F. Barry, D. Demille, “Laser cooling of a diatomic molecule,” Nature 467(7317), 820–823 (2010). [CrossRef] [PubMed]
  11. P. F. Barker, M. N. Shneider, “Optical microlinear accelerator for molecules and atoms,” Phys. Rev. A 64(3), 033408 (2001). [CrossRef]
  12. P. F. Barker, M. N. Shneider, “Slowing molecules by optical microlinear deceleration,” Phys. Rev. A 66(6), 065402 (2002). [CrossRef]
  13. J. Ramirez-Serrano, K. E. Strecker, D. W. Chandler, “Modification of the velocity distribution of H2 molecules in a supersonic beam by intense pulsed optical gradients,” Phys. Chem. Chem. Phys. 8(25), 2985–2989 (2006). [CrossRef] [PubMed]
  14. S. Kuma, T. Momose, “Deceleration of molecules by dipole force potential: a numerical simulation,” New J. Phys. 11(5), 055023 (2009). [CrossRef]
  15. Y. Yin, Q. Zhou, L. Deng, Y. Xia, J. Yin, “Multistage optical Stark decelerator for a pulsed supersonic beam with a quasi-cw optical lattice,” Opt. Express 17(13), 10706–10717 (2009). [CrossRef] [PubMed]
  16. R. Fulton, A. I. Bishop, M. N. Shneider, P. F. Barker, “Optical Stark deceleration of nitric oxide and benzene molecules using optical lattices,” J. Phys. At. Mol. Opt. Phys. 39(19), S1097–S1109 (2006). [CrossRef]
  17. T. Takekoshi, J. R. Yeh, R. J. Knize, “Quasi-electrostatic trap for neutral atoms,” Opt. Commun. 114(5-6), 421–424 (1995). [CrossRef]
  18. M. N. Shneider, P. F. Barker, S. F. Gimelshein, “Molecular transport in pulsed optical lattices,” Appl. Phys., A Mater. Sci. Process. 89(2), 337–350 (2007). [CrossRef]
  19. Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, P. W. Turner, “Power scaling of single frequency ytterbium-doped fiber master oscillator power amplifier sources up to 500W,” IEEE J. Sel. Top. Quantum Electron. 13(3), 546–551 (2007). [CrossRef]
  20. D. C. Clary, “A theory for the photodissociation of polyatomic molecules, with application to CF3I,” J. Chem. Phys. 84(8), 4288–4298 (1986). [CrossRef]
  21. J. R. Bochinski, E. R. Hudson, H. J. Lewandowski, G. Meijer, J. Ye, “Phase space manipulation of cold free radical OH molecules,” Phys. Rev. Lett. 91(24), 243001 (2003). [CrossRef] [PubMed]
  22. J. Yin, “Realization and research of optically-trapped quantum degenerate gases,” Phys. Rep. 430(1-2), 1–116 (2006). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited