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

Optics Express, Vol. 20, Issue 7, pp. 7792-7806 (2012)

http://dx.doi.org/10.1364/OE.20.007792

Acrobat PDF (2728 KB)

### 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 ~10^{7}Wcm^{−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

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

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

_{2}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 H_{2} 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]

_{4}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]

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]

^{7}Wcm

^{−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

**17**(13), 10706–10717 (2009). [CrossRef] [PubMed]

_{4}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]

## 2. Slowing scheme and its principle

*w*

_{0}= 50µm), which is created by two nearly counter-propagating, far-off-resonance, single-frequency, linear-polarized infrared lasers with an equal intensity of

*I*

_{0}= 1.02 × 10

^{7}Wcm

^{−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]

*z*axis. The velocity of the moving lattice is given by

*v*

_{latt}= (

*ω*

_{1}-

*ω*

_{2})/|

*ω*

_{1}and

*ω*

_{2}are their laser frequencies.

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]

*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*

_{1}(

*t*) and

*E*

_{2}(

*t*) are the amplitudes of the infrared lattice beam 1 and 2 respectively,

*q*= |

*δ*=

*d*(

*ω*

_{1}-

*ω*

_{2})/

*dt*is the frequency chirp, and

*v*

_{latt0}is the initial lattice velocity. In our scheme, the velocity of the moving lattice is a constant (i.e., the frequency difference (Δ

*ω*=

*ω*

_{1}-

*ω*

_{2}) of the two laser beams is also a constant), so we have

*δ*= 0.

*z*axis, they will experience an optical dipole interaction potential in the red-detuned optical lattice field as follows [6

**2**(7), 465–468 (2006). [CrossRef]

*I*

_{1}=

*I*

_{2}=

*I*

_{0}exp[-2(

*x*

^{2}+

*y*

^{2})/

*w*

_{0}

^{2}] is the intensity of each light field,

*w*

_{0}is the waist (i.e., the half-width at 1/

*e*

^{2}maximum intensity) of the laser beams,

*ε*

_{0}is the permittivity in free space,

*c*is the speed of light in vacuum, and

*k*= (4

*π*sin(

*β*/2))/

*λ*is the lattice wave-number. For CH

_{4}molecule, we have

*α*= 2.9 × 10

^{−40}Cm

^{2}/V.

*v*

_{latt}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.

*z*

_{r}) of the slowed molecules in the traveling optical lattice is defined as a synchronous phase angle

*ϕ*, where

*ϕ*=

*z*

_{r}/Λ × 360

^{°}and Λ is the spatial period of moving lattice. The point of

*z*

_{r}= 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 0

^{0}<

*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.

*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*=

*ϕ*

_{0}(where

*ϕ*

_{0}is the synchronous phase angle of the synchronized molecule, usually we choose 0

^{°}<

*ϕ*

_{0}≤180

^{°}), the lattice should be switched off rapidly, and then in the region of 0

^{°}<

*ϕ*≤

*ϕ*

_{0}, 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

*v*

_{latt}) should be reduced to another constant (until it reaches zero) by modulating Δ

*ω*, as shown in Fig. 1(b), and the velocity reduced amount of the lattice is denoted as Δ

*v*

_{latt}. In this paper, the initial velocity of the moving lattice is set as

*v*

_{latt0}=

*v*

_{m0}-Δ

*v*

_{latt}for each Δ

*v*

_{latt}, here

*v*

_{m0}is the initial central velocity (240m/s) of incident molecular beam in our simulations. If Δ

*v*

_{latt}is equal to 80m/s [see Fig. 1(b)], we will have

*v*

_{latt0}= 160m/s. In the deceleration process, for

*ϕ*

_{0}= 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

*v*

_{latt}should be reduced to 80m/s and then to 0m/s. Also, for

*ϕ*

_{0}= 120

^{°},

*v*

_{latt}should be reduced to 80m/s and then to 0m/s when

*t*= 67μs and 137μs.

## 3. Results of 3D Monte-Carlo simulation

_{4}) 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]

*w*

_{0}= 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 CF_{3}I,” J. Chem. Phys. **84**(8), 4288–4298 (1986). [CrossRef]

*z*axis.

*m*= 23122, the synchronous phase angle is

*ϕ*

_{0}= 90

^{°}, the velocity reduced amount of the traveling lattice is Δ

*v*

_{latt}= 80m/s, and the initial lattice velocity is

*v*

_{latt0}= 160m/s (i.e.,

*v*

_{latt0}= 240m/s-Δ

*v*

_{latt}), 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) . 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

*v*

_{l}= 0.9m/s,

*T*

_{l}= 11.5μK, and

*n*= 5.27 × 10

^{−6}(

*n*=

*N*/

*N*

_{0}, where

*N*and

*N*

_{0}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

*v*

_{latt}is reduced from 160m/s to 80m/s, and the packet 2 is the second outcome when

*v*

_{latt}is reduced from 80m/s to 0m/s), and their central velocities are

*v*

_{l}= 160.7m/s and

*v*

_{l}= 80.3m/s, respectively. From Fig. 2(a), we can find that the temperatures

*T*

_{l}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

*T*

_{l}and

*n*are lower than those of the packet 2. We also study the deceleration effects when

*ϕ*

_{0}= 120

^{°}, and obtain some similar results as

*ϕ*

_{0}= 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

*ϕ*

_{0}= 90

^{°}) can be used to decelerate CH

_{4}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

*v*

_{l}= 0.925m/s,

*T*

_{l}= 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.

*m*, and the simulated results are shown in Fig. 3 . Figure 3(a) shows the relationship between the molecular velocity

*v*

_{m}and the stage number

*m*when the initial velocity of the traveling lattice is

*v*

_{latt0}= 160m/s and its velocity reduced amount is Δ

*v*

_{latt}= 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

*ϕ*

_{0}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]

*m*, the temperature

*T*

_{l}of the slowed molecular packet will be reduced gradually, and the larger the synchronous phase angle

*ϕ*

_{0}is, the lower the temperature

*T*

_{l}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.

*ϕ*

_{0}= 120

^{°}than that with

*ϕ*

_{0}= 90

^{°}, and the slowed effects (

*v*

_{l},

*n*and

*T*

_{l}) with

*ϕ*

_{0}= 120

^{°}are greatly better than that with

*ϕ*

_{0}= 90

^{°}.

*m*that need to slow a subsonic CH

_{4}molecular beam from 240m/s to zero (i.e., to obtain the slowest packet) on the velocity reduced amount Δ

*v*

_{latt}of the traveling lattice, the synchronous phase angle

*ϕ*

_{0}and the input power

*P*

_{0}of lattice beams, and the simulated results are shown in Fig. 4 . We can see from Fig. 4(a) that with the increase of Δ

*v*

_{latt}, the needed deceleration-stage number

*m*will be increased gradually when

*P*

_{0}= 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

*ϕ*

_{0}= 150

^{°}. So in our simulations,

*ϕ*

_{0}= 90

^{°}and

*ϕ*

_{0}= 120

^{°}are employed to demonstrate our deceleration scheme and study its slowing results (see Figs. 2, 3, and later Fig. 5 ). It can be found from Fig. 4(b) that with the increase of

*ϕ*

_{0}, the needed deceleration-stage number

*m*will be decreased gradually when

*P*

_{0}= 400W, and when the synchronous phase angle

*ϕ*

_{0}is given, the smaller the velocity reduced amount Δ

*v*

_{latt}of the moving lattice is, the less the needed deceleration-stage number will be. In particular, when

*ϕ*

_{0}= 150

^{°}and Δ

*v*

_{latt}= 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 Δ

*v*

_{latt}is, the more the obtained cold molecules in the slowest packet will be. So Δ

*v*

_{latt}= 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

*P*

_{0}is, and the smaller the velocity reduced amount Δ

*v*

_{latt}is, the less the needed deceleration-stage number

*m*will be.

*m*that needs to slow a subsonic molecular beam from 240/s to 0m/s is not only relative to the velocity reduced amount Δ

*v*

_{latt}of the moving lattice and its power

*P*

_{0}, but also to the synchronous phase angle

*ϕ*

_{0}, and when the velocity reduced amount Δ

*v*

_{latt}is smaller, and the synchronous phase angle

*ϕ*

_{0}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 Δ

*v*

_{latt}and

*ϕ*

_{0}.

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

*t*

_{r}of laser lattice pulse to reach its maximum intensity and a falling time

*t*

_{f}of laser pulse to zero. We investigate the influence of

*t*

_{r}and

*t*

_{f}on the slowing results, including the final central velocity, the fraction and the temperature of slowed molecules provided that

*t*

_{r}is equal to

*t*

_{f}, and the simulated results are shown in Fig. 5. We can find from Fig. 5(a) that with the increase of

*t*

_{r}and

*t*

_{f}, the final velocity

*v*of the slowed packet will first drop and then rise, and for different synchronous phase angles such as

_{l}*ϕ*

_{0}= 60

^{°},

*ϕ*

_{0}= 90

^{°},

*ϕ*

_{0}= 120

^{°}and

*ϕ*

_{0}= 150

^{°}, and the turning points appear at

*t*

_{r}=

*t*

_{f}= 4.0ns, 1.5ns, 0.8ns and 0.4ns respectively. In order to explain these results, we use

*ϕ*

_{0}= 90

^{°}as an example [see Fig. 5(d)]. Figure 5(d) shows the optical dipole force experienced by molecules on the

*z*axis in one spatial period of traveling lattice. The region of 0

^{°}<

*ϕ*<180

^{°}(the rear half of each lattice cell) is the decelerating phase-angle region for molecules in the red-detuned lattice. For

*ϕ*

_{0}= 90

^{°}, if the laser pulses have top-hat temporal shape, the lattice light can be switched on completely when the synchronized molecules arrive at

*ϕ*= 0

^{°}and can also be switched off 100% when they reach the position of

*ϕ*= 90

^{°}. However, for the laser pulses with a time-dependent intensity, the lattice field cannot reach its maximum intensity immediately due to the existence of

*t*

_{r}and can also not be reduced to zero in time when the synchronized molecules arrive at

*ϕ*= 90

^{°}owing to

*t*

_{f}. Here we assume that a group of molecules travel from point A to B within the time

*t*

_{r}and from A’ to B’ within

*t*

_{f}, as shown in Fig. 5(d). In this case, when the molecules move from A to B, the deceleration effect of the molecules owing to

*t*

_{r}will be poorer than that in the case of the rising time

*t*

_{r}= 0 (i.e., the top-hat temporal shape), while the molecules are in the motion of A’→B’, they will still be exposed to the interaction of the lattice field and still be decelerated due to the existence of

*t*

_{f}, and then the slowing effect due to

*t*

_{f}will be far better than that in the case of the falling time

*t*

_{f}= 0 (i.e., the top-hat temporal shape). However, it is clear from Fig. 5(d) that the optical dipole force

*F*

_{z}experienced by the molecules in the motion of A’→B’ is larger than that in A→B, That is, an appropriate

*t*

_{r}(and

*t*

_{f}) will make the deceleration effect increased by

*t*

_{f}be greater than the loss of the slowing effect resulted from

*t*

_{r}, so a pair of appropriate

*t*

_{r}and

*t*

_{f}will lead to a better slowing effect than that produced by the top-hat temporal laser pulses. However, when

*t*

_{r}and

*t*

_{f}are too long, the deceleration effect increased by

*t*

_{f}will be equal to the loss of the slowing effect resulted from

*t*

_{r}. Also, they will shallow the optical lattice potential significantly and even lead to the acceleration of molecules in the next accelerating phase angle region of −180

^{°}<

*ϕ*<0

^{°}. Thus the slowing effect will be declined seriously.

*ϕ*

_{0}is, the shorter the rising and falling times (

*t*

_{r}and

*t*

_{f}) of laser pulses contributing to the slowing of molecules will be. Thus the turning point with

*ϕ*

_{0}= 150

^{°}appears earlier than one with other synchronous phase angles such as

*ϕ*

_{0}= 120

^{°},

*ϕ*

_{0}= 90

^{°}and

*ϕ*

_{0}= 60

^{°}on the horizontal axis. As shown in Fig. 5(b), with the increase of

*ϕ*

_{0}, the turning point of

*t*

_{r}and

*t*

_{f}will be lower and lower.

*t*

_{r}and

*t*

_{f}on the temperature

*T*

_{l}of the slowed packet and fraction

*n*of cold molecules when

*ϕ*

_{0}= 90

^{°}and the final most-probable velocity

*v*

_{l}of slowed molecules is below 1m/s. It is clear that with increase of

*t*

_{r}and

*t*

_{f}, both

*T*

_{l}and

*n*decrease gradually. This is because

*t*

_{r}and

*t*

_{f}will result in more shallow optical potentials in the deceleration process, so that less cold molecules can be trapped and

*T*

_{l}of the slowed packet will also be lower.

## 5. Discussion

**17**(13), 10706–10717 (2009). [CrossRef] [PubMed]

_{4}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 CH

_{4}beam, and the simulated results are shown in Fig. 6 . In our simulations and comparison, we use the same lattice parameters and incident pulsed subsonic CH

_{4}beam, and for the quasi-cw traveling lattice, the velocity reduced amount of the traveling lattice is chosen as Δ

*v*

_{latt}= 80m/s (i.e., its initial velocity is

*v*

_{latt0}= 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 CH

_{4}beam from 240m/s to about 0.9m/s, but the static one can only be used to slow the CH

_{4}beam from 240m/s to ~195.5m/s.

*m*= 40000 (i.e., a lattice length of about 2.13cm) is needed to slow a subsonic beam from 240m/s to ~0m/s.

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

*δ*= 0) by 1D Monte-Carlo simulation, and the results are shown in Fig. 7 . In the simulations, we take molecule I

_{2}as an example and the pulsed I

_{2}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

*I*

_{0}= 6.4 × 10

^{7}Wcm

^{−2},

*ϕ*

_{0}= 90

^{°}and Δ

*v*

_{latt}= 100m/s.

*n*of cold molecules are

*T*

_{l}= 6.08μK and

*n*= 0.15%, respectively. Figure 7(b) shows the deceleration results of a chirped optical lattice when

*I*

_{0}= 12 × 10

^{9}Wcm

^{−2},

*ψ*= 0.735,

*δ*= 5.28 × 10

^{15}rad/s and

*q*= 1.56 × 10

^{7}/m which are the same as ones used in Ref. [12

**66**(6), 065402 (2002). [CrossRef]

*T*

_{l}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

*T*

_{l}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

^{7}Wcm

^{−2}. By using 3D Monte-Carlo method, we have studied the slowing results (including the final central velocity

*v*

_{l}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 Δ

*v*

_{latt}of the traveling lattice and its power as well as the synchronous phase angle

*ϕ*

_{0}. 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

*ϕ*

_{0}. This shows that when the molecular number in an incident molecular pulse is equal to 10

^{12}, our obtainable number of cold molecules in the slowed packet can reach 10

^{5}~10

^{6}. We have also found that the larger the synchronous phase angle

*ϕ*

_{0}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

*ϕ*

_{0}, a smaller Δ

*v*

_{latt}, or a higher

*P*

_{0}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

*t*

_{r}and the falling time

*t*

_{f}, the final velocity

*v*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 (

_{l}*t*

_{r}and

*t*

_{f}) of laser pulses contributing to the slowing of molecules will be. (3) A pair of appropriate

*t*

_{r}and

*t*

_{f}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

**66**(6), 065402 (2002). [CrossRef]

^{5}~10

^{6}. 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]

## Acknowledgment

## References and links

1. | U. Schlöder, C. Silber, and C. Zimmermann, “Photoassociation of heteronuclear lithium,” Appl. Phys. B |

2. | C. A. Regal, C. Ticknor, J. L. Bohn, and D. S. Jin, “Creation of ultracold molecules from a Fermi gas of atoms,” Nature |

3. | D. C. Weinstein, J. Marden, F. Carnevali, and A. Hemmati-Brivanlou, “Magnetic trapping of calcium monohydride molecules at millikelvin temperatures,” Nature |

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. |

5. | N. Vanhaecke, U. Meier, M. Andrist, B. H. Meier, and F. Merkt, “Multistage Zeeman deceleration of hydrogen atoms,” Phys. Rev. A |

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. |

7. | Y. Liu, M. Yun, Y. Xia, L. Deng, and J. Yin, “Experimental generation of a cw cold CH |

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 |

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 |

10. | E. S. Shuman, J. F. Barry, and D. Demille, “Laser cooling of a diatomic molecule,” Nature |

11. | P. F. Barker and M. N. Shneider, “Optical microlinear accelerator for molecules and atoms,” Phys. Rev. A |

12. | P. F. Barker and M. N. Shneider, “Slowing molecules by optical microlinear deceleration,” Phys. Rev. A |

13. | J. Ramirez-Serrano, K. E. Strecker, and D. W. Chandler, “Modification of the velocity distribution of H |

14. | S. Kuma and T. Momose, “Deceleration of molecules by dipole force potential: a numerical simulation,” New J. Phys. |

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 |

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. |

17. | T. Takekoshi, J. R. Yeh, and R. J. Knize, “Quasi-electrostatic trap for neutral atoms,” Opt. Commun. |

18. | M. N. Shneider, P. F. Barker, and S. F. Gimelshein, “Molecular transport in pulsed optical lattices,” Appl. Phys., A Mater. Sci. Process. |

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. |

20. | D. C. Clary, “A theory for the photodissociation of polyatomic molecules, with application to CF |

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. |

22. | J. Yin, “Realization and research of optically-trapped quantum degenerate gases,” Phys. Rep. |

**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

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### References

- U. Schlöder, C. Silber, C. Zimmermann, “Photoassociation of heteronuclear lithium,” Appl. Phys. B 73(8), 801–805 (2001). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- E. S. Shuman, J. F. Barry, D. Demille, “Laser cooling of a diatomic molecule,” Nature 467(7317), 820–823 (2010). [CrossRef] [PubMed]
- P. F. Barker, M. N. Shneider, “Optical microlinear accelerator for molecules and atoms,” Phys. Rev. A 64(3), 033408 (2001). [CrossRef]
- P. F. Barker, M. N. Shneider, “Slowing molecules by optical microlinear deceleration,” Phys. Rev. A 66(6), 065402 (2002). [CrossRef]
- 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]
- S. Kuma, T. Momose, “Deceleration of molecules by dipole force potential: a numerical simulation,” New J. Phys. 11(5), 055023 (2009). [CrossRef]
- 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]
- 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]
- T. Takekoshi, J. R. Yeh, R. J. Knize, “Quasi-electrostatic trap for neutral atoms,” Opt. Commun. 114(5-6), 421–424 (1995). [CrossRef]
- 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]
- 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]
- D. C. Clary, “A theory for the photodissociation of polyatomic molecules, with application to CF3I,” J. Chem. Phys. 84(8), 4288–4298 (1986). [CrossRef]
- 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]
- J. Yin, “Realization and research of optically-trapped quantum degenerate gases,” Phys. Rep. 430(1-2), 1–116 (2006). [CrossRef]

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