## Heating and phase-space decompression of evanescent-wave cooled atoms by multiple photon reabsorption

Optics Express, Vol. 11, Issue 16, pp. 1827-1834 (2003)

http://dx.doi.org/10.1364/OE.11.001827

Acrobat PDF (97 KB)

### Abstract

We show that multiple reabsorption of resonance-frequency photons in a cloud of evanescent-wave cooled atoms can have a significant influence on the cooling efficiency and maximum value of the atomic phase-space density.

© 2003 Optical Society of America

## 1. Introduction

1. J. Söding, R. Grimm, and Yu. B. Ovchinnikov, “Gravitational laser trap for atoms with evanescent-wave cooling,” Opt. Commun. **119**, 652–662 (1995). [CrossRef]

7. M. Hammes, D. Rychtarik, B. Engeser, H.-C. Nägel, and R. Grimm, “Evanescent-Wave Trapping and Evaporative Cooling of an Atomic Gas at the Crossover to Two Dimensions,” Phys. Rev. Lett. **90**, 173001-1-4 (2003). [CrossRef] [PubMed]

7. M. Hammes, D. Rychtarik, B. Engeser, H.-C. Nägel, and R. Grimm, “Evanescent-Wave Trapping and Evaporative Cooling of an Atomic Gas at the Crossover to Two Dimensions,” Phys. Rev. Lett. **90**, 173001-1-4 (2003). [CrossRef] [PubMed]

9. P. Domokos and H. Ritsch, “Efficient laoding and cooling in a dynamic optical evanescent-wave microtrap,” Europhys. Lett. **54**, 306–312 (2001). [CrossRef]

13. L. Khaykovich and N. Davidson, “Adiabatic focusing of cold atoms in a blue-detuned laser standing wave,” Appl. Phys. B **70**, 683–688 (2000). [CrossRef]

14. S. Meneghini, V. I. Savichev, K. A. H. van Leeuwen, and W. P. Schleich, “Atomic focusing and near field imaging: A combination for producing small-period nanostructures,” Appl. Phys. B **70**, 675–682 (2000). [CrossRef]

15. A. Lenef, T. D. Hammond, E. T. Smith, M. S. Chapman, R. A. Rubenstein, and D. E. Pritchard, “Rotation Sensing with an Atom Interferometer,” Phys. Rev. Lett **78**, 760–763 (1997). [CrossRef]

17. A. Peters, K. Y. Chung, and S. Chu, “Measurement of gravitational acceleration by dropping atoms,” Nature **400**, 849–852 (1999). [CrossRef]

18. T. Calarco, E. A. Hinds, D. Jaksch, J. Schmiedmayer, J. I. Cirac, and P. Zoller, “Quantum gates with neutral atoms: Controlling colisional interactions in time-dependent traps,” Phys. Rev. A **61**, 022304-1-11 (2000). [CrossRef]

19. M. D. Lukin, M. Fleischhauer, and R. Cote, “Dipole blockade and Quantum Information Processing in Mesoscopic Atomic Ensembles,” Phys. Rev. Lett **87**, 037901-1-4 (2001). [CrossRef] [PubMed]

1. J. Söding, R. Grimm, and Yu. B. Ovchinnikov, “Gravitational laser trap for atoms with evanescent-wave cooling,” Opt. Commun. **119**, 652–662 (1995). [CrossRef]

6. M. Hammes, D. Rychtarik, H.-C. Nägel, and R. Grimm, “Cold-atom gas at very high densities in an optical surface microtrap,” Phys. Rev. A **66**, 051401-1-4 (2002). [CrossRef]

7. M. Hammes, D. Rychtarik, B. Engeser, H.-C. Nägel, and R. Grimm, “Evanescent-Wave Trapping and Evaporative Cooling of an Atomic Gas at the Crossover to Two Dimensions,” Phys. Rev. Lett. **90**, 173001-1-4 (2003). [CrossRef] [PubMed]

*et al.*in [1

1. J. Söding, R. Grimm, and Yu. B. Ovchinnikov, “Gravitational laser trap for atoms with evanescent-wave cooling,” Opt. Commun. **119**, 652–662 (1995). [CrossRef]

**119**, 652–662 (1995). [CrossRef]

20. M. V. Subbotin, V. I. Balykin, D. V. Laryushin, and V. S. Letokhov, “Laser controlled atom waveguide as a source of ultracold atoms,” Opt. Commun. **139**, 107–116 (1997). [CrossRef]

22. J. Yin, Y. Zhu, and Y. Wang, “Gravito-optical trap for cold atoms with doughnut-hollow-beam cooling,” Phys. Lett. A **248**, 309–318 (1998). [CrossRef]

^{133}Cs in a gravito-optical surface trap. In Section 4, we discuss the implication of the reabsorption effect on the cooling of atoms on an evanescent wave.

## 2. Evanescent-wave cooling and multiple photon reabsorption

**119**, 652–662 (1995). [CrossRef]

*λ*/4

*π*)(

*n*

^{2}sin

^{2}

*θ*-1)

^{-1/2}. Here

*λ*is the wavelength,

*n*the index of refraction of the dielectric, and

*θ*the angle of incidence of the reflected beam. Considering alkali atoms, we assume the evanescent wave to be tuned above the D

_{2}-resonance frequency by an amount

*δ*with respect to the lower hyperfine ground state |

*g*1〉. The low-power repumping beam can be tuned into resonance with the transition from the upper hyperfine ground state |

*g*2〉 to the excited state |

*e*〉 (in experiments with Cs it is usually the

*F*=4→

*F*′=4 transition) in order to optically pump atoms that have entered |

*g*2〉 back into the state |

*g*1〉. If an atom in the state |

*g*1〉 enters the repulsive evanescent wave and, near the turning point, makes a transition to the state |

*g*2〉 (through scattering of an evanescent-wave photon), the energy lost by the atom as it moves up the potential will be larger than that it gains when leaving the field after the reflection. Recycling the process leads to a cooling of the atomic sample at the rate [1

**119**, 652–662 (1995). [CrossRef]

*δ*is the ground-state hyperfine splitting and

_{hfs}*q*is the mean branching ratio to the lower hyperfine ground state for the elastic scattering of a photon. The parameter τ

_{e}*denotes the mean time between incoherent reflections. In the case of gravitational confinement of the atoms on the evanescent-wave mirror, this parameter is given by*

_{c}*m*the atom’s mass,

*g*the acceleration of gravity, and

*φ*the angle between the vertical axis and the vacuum-dielectric interface. In contrast to Ref. [1

**119**, 652–662 (1995). [CrossRef]

*φ*is in the denominator and, therefore, when

*φ*approaches zero, the time τ

*goes to infinity, since in this case gravity can no longer return the reflected atoms back to the evanescent wave. Equation (2) is derived from the equation of conservation of energy, similar to that considered in Ref. [1*

_{c}**119**, 652–662 (1995). [CrossRef]

*g*2〉-state atoms on their way up in the gravitational field, is calculated to be

*q*is the mean branching ratio to the state |

_{r}*g*1〉 for transitions in the repumping field starting from the state |

*g*2〉,

*k*the Boltzmann’s constant, and

_{B}*T*the instantaneous temperature of the atoms. We point out that, in our calculations, the rate

*γ*in Eq. (3) turns out to be twice that given in equation (13) of Ref. [1

_{geo}**119**, 652–662 (1995). [CrossRef]

**119**, 652–662 (1995). [CrossRef]

*T*will give the final temperature

*T*Since Eq. (4) does not contain the contribution of the heating caused by the reabsorption of photons emitted by the atoms in the repumping process,

_{eq.}*T*can be considered to be correct for low atomic densities.

_{eq}*g*1〉 [1

**119**, 652–662 (1995). [CrossRef]

*g*2〉 pass the sample with a negligibly small probability to be absorbed or Raman scattered, since they are far enough from resonance with the transition |

*g*1〉→|

*e*〉. As each cooling cycle ends with a transition |

*e*〉→|

*g*1〉, there will be resonant photons produced with a rate

*R*

_{1}=(1-

*q*)/τ

_{e}*. The higher the density of atoms in the cloud, the higher is the probability that these photons will be absorbed by the atoms. These photons are created in spontaneous transitions and are emitted in all directions with equal probability. Since they originally appear in a very thin layer above the evanescent-wave mirror, only a fraction of them,*

_{c}*η*≈1/2, enter the sample. The mean rate at which the resonant photons get into the sample is, therefore,

_{in}*R*=

_{in}*η*

_{in}R_{1}.

*R*of resonant-photon emissions per atom is equal to the sum of

_{rad}*R*and

_{in}*R*, where

_{r}*R*is the additional rate due to multiple reabsorption events. The mean power of the resonance-frequency radiation emitted by each atom is, therefore,

_{r}*P*=2

_{rad}*πℏv*

_{1}

*R*, where

_{rad}*v*

_{1}is the resonant-photon frequency. A part of this radiation continuously escapes the sample at a power of

*P*=

_{out}*η*, where

_{out}P_{rad}*η*

_{out}is smaller than 1. Since each absorption of a resonance-frequency photon is followed by emission of another such photon, energy conservation requires that the radiation power entering the sample,

*P*≡2

_{in}*πℏv*

_{1}

*R*, has to be equal to the escaping power

_{in}*P*. Thus we obtain

_{out}*η*is known, we now calculate the rate of heating of the atoms in the reabsorption events. This rate is given by

_{out}*γ*=(Δ

_{r}*T*/

_{r}*T*)

*R*, where Δ

_{r}*T*is the temperature change caused by optical recoils during the time 1/

_{r}*R*. On average, each atom in this time absorbs and emits one resonant photon, in total undergoing a mean number of 2/

_{r}*q*transitions between the ground and the excited state (due to the presence of the repumping field). Each of the transitions is associated with an increase of the atomic kinetic energy by one recoil energy. Thus, Δ

_{r}*T*=(2/

_{r}*q*)(2

_{r}*E*/3

_{rec}*k*). By making use of Eq. (6) and writing

_{B}*R*and

_{in}*E*in their explicit forms, we obtain

_{rec}*γ˜*=

_{heat}*γ*+

_{heat}*γ*, where

_{r}*γ*is given by Eq. (4). Taking into account the fact that

_{heat}*η*≈1/2, we obtain

_{in}*η*in the denominator of the second term. Since

_{out}*η*is always smaller than unity, the rate

_{out}*γ˜*is always higher than

_{heat}*γ*, and only if resonance-photon reabsorption can be neglected is

_{heat}*η*≈1 and

_{out}*γ˜*≈

_{heat}*γ*.

_{heat}*γ˜*=

_{heat}*γ*+

_{Sis}*γ*. This can be written in the form showing the explicit dependence of the equilibrium temperature

_{geo}*T̃*on the parameter

_{eq}*η*

_{out}*η*≡

_{out}*P*/

_{out}*P*, which may itself depend on

_{rad}*T̃*. To calculate

_{eq}*η*, we assume that the atomic sample has a constant density equal to the peak density

_{out}*n*

_{0}within the effective trap volume. Then, by modelling the emitted resonance-frequency photons as spherical waves, continuously radiated by each atom at power

*P*, we can estimate the mean power

_{rad}*P*and thus find

_{out}*η*. In these calculations, the attenuation of the waves with the distance of propagation has to be taken into account. The attenuation coefficient for the weak resonance-frequency radiation is given by

_{out}*α*=σ

_{res}n_{0}, where σ

*≈3*

_{res}*λ*

^{2}/2

*π*is the atomic absorption cross section corresponding to a lifetime broadened transition. The procedure for calculating

*η*is outlined in Section 3 assuming the geometry of a horizontally aligned gravito-optical surface trap.

_{out}## 3. Cooling in a gravito-optical surface trap

2. Yu. B. Ovchinnikov, I. Manek, and R. Grimm, “Surface Trap for Cs atoms based on Evanescent-Wave Cooling,” Phys. Rev. Lett. **79**, 2225–2228 (1997). [CrossRef]

23. I. Manek, Yu. B. Ovchinnikov, and R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Commun. **147**, 67–70 (1998). [CrossRef]

*D*is usually on the order of 1 mm and, therefore, when the atoms are cooled down, the effective vertical size of the sample,

*u*=

*k*/

_{B}T*mg*, turns out to be much smaller than

*D*. In this case, the calculation of the parameter

*η*becomes particularly simple, since

_{out}*D*can be extended to infinity. The atomic sample can thus be considered to be in the form of an infinite slab with thickness

*u*. Applying the calculation technique described in the previous Section, the average radiated power per one atom leaving the sample through the slab surfaces is obtained in the form

*z*denotes the coordinate along the normal to the slab and Γ(0,

*α*u) is the incomplete gamma function. Equation (12) can in fact be cast in an approximate form, which, while still being quite accurate, allows a more transparent interpretation,

*αu*approaches zero and

*P*approaches its maximum value of

_{out}*P*, as it should. On the other hand, for strong absorption,

_{rad}*αu*is much larger than 1 and

*P*approaches zero. The attenuation coefficient

_{out}*α*=3

*λ*

^{2}

*n*

_{0}/2

*π*depends on the atomic density

*n*

_{0}=

*N*/(

*uπD*

^{2}/4) with

*N*being the total number of atoms in the trap. The product

*αu*is, therefore, independent of

*u*and Eq. (13) can be rewritten in terms of

*N*as

*β*=6

*λ*

^{2}/(

*πD*)

^{2}. We remind that this equation is valid for

*u*≪

*D*. Substituting Eq. (14) into Eq. (9), we obtain an expression for the equilibrium temperature

*T̃*, which will now be a function of

_{eq}*N*and

*D*.

^{133}Cs in a trap that was recently used in experiments by M. Hammes

*et al.*[6

6. M. Hammes, D. Rychtarik, H.-C. Nägel, and R. Grimm, “Cold-atom gas at very high densities in an optical surface microtrap,” Phys. Rev. A **66**, 051401-1-4 (2002). [CrossRef]

**90**, 173001-1-4 (2003). [CrossRef] [PubMed]

*D*of their hollow beam was 0.8 mm and the evanescent-wave detuning was

*δ*=2

*π*×5 GHz. For

^{133}Cs the ground-state hyperfine splitting is

*δ*=2

_{hfs}*π*×9.2 GHz, the spontaneous decay rate Γ=2

*π*×5.3 MHz, the resonance wavelength

*λ*=852 nm, the mass

*m*=2.2×10

^{-25}kg, and the branching ratios are

*q*=0.75 and

_{e}*q*=0.611 [1

_{r}**119**, 652–662 (1995). [CrossRef]

*φ*=

*π*/2, and obtain a value of

*T*=1

_{eq}*µ*K, independent of the number of the trapped atoms. The lowest temperature which has been achieved so far in the experiments with low-density atomic samples of

^{133}Cs is two times higher than this calculated value [3]. One of the possible reasons could be the “roughness” of the realistic evanescent-wave mirror which leads to a diffuse atomic reflection [11

11. C. Henkel, K. Mølmer, R. Kaiser, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Diffuse atomic reflection at a rough mirror,” Phys. Rev. A **55**, 1160–1178 (1997). [CrossRef]

*φ*in Eq. (3)). We now include the reabsorption processes and numerically solve Eq. (9), using Eq. (14) for

*η*. The temperature

_{out}*T̃*calculated in this way is shown as a function of

_{eq}*N*in Fig. 2(a) (

*T̃*(

_{eq}*N*) for small values of

*N*is shown in the inset). The resonance-photon reabsorption is seen to significantly affect the final temperature of the cooled atoms. The lowest possible temperature in cooling of, e.g., 10

^{8}atoms turns out to be almost two orders of magnitude higher than

*T*given by Eq. (5). At large values of

_{eq}*N*, which provide small

*η*, the temperature

_{out}*T̃*shows a linear dependence on

_{eq}*N*with a slope given by

*N*≤4×10

^{6}. If we substitute

*δ*=2

*π*×3 GHz and

*D*=0.52 mm as applied in Ref. [3] into Eq. (15), we obtain

*a*≈2×10

^{-12}K. This compares well with the measured value of 1.5×10

^{-12}K.

*n*

_{0}of the atoms scales as

*N*/

*T̃*(

_{eq}*n*

_{0}=4

*N*/

*uπD*

^{2}) and it is plotted as a function of

*N*in Fig. 2(b). The function

*n*

_{0}(

*N*) has a local maximum at

*N*≈8×10

^{6}, since at that point the relative increase of temperature, d

*T̃*/

_{eq}*T̃*, starts to exceed the relative growth of

_{eq}*N*. When

*N*increases further, the density

*n*

_{0}slowly drops towards a constant value. This value can be determined to be

*n*

_{∞}=4

*mg*/

*ak*

_{B}πD^{2}≈3×10

^{17}. However, for

*N*>10

^{8}the height

*u*of the sample starts to exceed the diameter

*D*and, therefore, Eq. (14) cannot be used anymore.

*n*

_{0}and

*T̃*as Ω=(

_{eq}*n*

_{0}/7)(

*2πℏ*

^{2}/

*mk*)

_{B}T̃_{eq}^{3/2}. Figure 3a shows the dependence of Ω on

*N*for

*N*<2×10

^{7}. The maximum value of Ω is reached at

*N*≈1.8×10

^{6}. We note that in Ref. [6

6. M. Hammes, D. Rychtarik, H.-C. Nägel, and R. Grimm, “Cold-atom gas at very high densities in an optical surface microtrap,” Phys. Rev. A **66**, 051401-1-4 (2002). [CrossRef]

*N*=2×10

^{6}in Ref. [6

**66**, 051401-1-4 (2002). [CrossRef]

*u*of the sample is much smaller than the diameter

*D*, when

*N*corresponds to a high value of Ω. Therefore, changing

*D*does not result in a significant change of the maximum achievable phase-space density (Ω

*). If, on the other hand, there would be some mechanism that would reduce the height*

_{max}*u*, the value of Ω

*could be increased. As an example, we show the dependence of Ω on*

_{max}*N*for atoms acted on by an additional force

**f**=10×

*m*(Fig. 3b). This force can be created, e.g., by a spatially inhomogeneous far-red-detuned laser field, similar to one used in Ref. [7

**g****90**, 173001-1-4 (2003). [CrossRef] [PubMed]

## 4. Discussion

20. M. V. Subbotin, V. I. Balykin, D. V. Laryushin, and V. S. Letokhov, “Laser controlled atom waveguide as a source of ultracold atoms,” Opt. Commun. **139**, 107–116 (1997). [CrossRef]

21. H. Nha and W. Jhe, “Sisyphus cooling on the surface of a hollow-mirror atom trap,” Phys. Rev. A **56**, 729–736 (1997). [CrossRef]

24. D. J. Harris and C. M. Savage, “Atomic gravitational cavities from hollow optical fibers,” Phys. Rev. A **51**, 3967–3971 (1995). [CrossRef] [PubMed]

*η*will be more complicated than that given in Section 3 for the gravito-optical surface trap.

_{out}## Acknowledgments

## References and links

1. | J. Söding, R. Grimm, and Yu. B. Ovchinnikov, “Gravitational laser trap for atoms with evanescent-wave cooling,” Opt. Commun. |

2. | Yu. B. Ovchinnikov, I. Manek, and R. Grimm, “Surface Trap for Cs atoms based on Evanescent-Wave Cooling,” Phys. Rev. Lett. |

3. | M. Hammes, D. Rychtarik, V. Druzhinina, U. Moslener, I. Manek-Hönninger, and R. Grimm, “Optical and evaporative cooling of caesium atoms in the gravito-optical surface trap,” J. Mod. Opt. |

4. | P. Desbiolles, M. Arndt, P. Szriftgiser, and J. Dalibard, “Elementary Sisyphus process close to a dielectric surface,” Phys. Rev. A |

5. | R. J. C. Spreeuw, D. Voigt, B. T. Wolschrijn, and H. B. van Linden den Heuvell, “Creating a low-dimensional quantum gas using dark states in an inelastic evanescent-wave mirror,” Phys. Rev. A |

6. | M. Hammes, D. Rychtarik, H.-C. Nägel, and R. Grimm, “Cold-atom gas at very high densities in an optical surface microtrap,” Phys. Rev. A |

7. | M. Hammes, D. Rychtarik, B. Engeser, H.-C. Nägel, and R. Grimm, “Evanescent-Wave Trapping and Evaporative Cooling of an Atomic Gas at the Crossover to Two Dimensions,” Phys. Rev. Lett. |

8. | H. Gauck, M. Hartl, D. Schneble, H. Schnitzler, T. Pfau, and J. Mlynek, “Quasi-2D Gas of Laser Cooled Atoms in a Planar Matter Waveguide,” Phys. Rev. Lett. |

9. | P. Domokos and H. Ritsch, “Efficient laoding and cooling in a dynamic optical evanescent-wave microtrap,” Europhys. Lett. |

10. | M. Gorliki, S. Feron, V. Lorent, and M. Dukloy, “Interferometric approaches to atom-surface van der Waals interactions in atomic mirrors,” hys. Rev. A |

11. | C. Henkel, K. Mølmer, R. Kaiser, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Diffuse atomic reflection at a rough mirror,” Phys. Rev. A |

12. | V. Savalli, D. Stevens, J. Estève, P. D. Featonby, V. Josse, N. Westbrook, C. I. Westbrook, and A. Aspect, “Specular Reflection of Matter Waves from a Rough Mirror,” Phys. Rev. Lett |

13. | L. Khaykovich and N. Davidson, “Adiabatic focusing of cold atoms in a blue-detuned laser standing wave,” Appl. Phys. B |

14. | S. Meneghini, V. I. Savichev, K. A. H. van Leeuwen, and W. P. Schleich, “Atomic focusing and near field imaging: A combination for producing small-period nanostructures,” Appl. Phys. B |

15. | A. Lenef, T. D. Hammond, E. T. Smith, M. S. Chapman, R. A. Rubenstein, and D. E. Pritchard, “Rotation Sensing with an Atom Interferometer,” Phys. Rev. Lett |

16. | M. Özcan, “Influence of electric potentials on atom interferometers: Increased rotation sensitivity,” J. Appl. Phys. |

17. | A. Peters, K. Y. Chung, and S. Chu, “Measurement of gravitational acceleration by dropping atoms,” Nature |

18. | T. Calarco, E. A. Hinds, D. Jaksch, J. Schmiedmayer, J. I. Cirac, and P. Zoller, “Quantum gates with neutral atoms: Controlling colisional interactions in time-dependent traps,” Phys. Rev. A |

19. | M. D. Lukin, M. Fleischhauer, and R. Cote, “Dipole blockade and Quantum Information Processing in Mesoscopic Atomic Ensembles,” Phys. Rev. Lett |

20. | M. V. Subbotin, V. I. Balykin, D. V. Laryushin, and V. S. Letokhov, “Laser controlled atom waveguide as a source of ultracold atoms,” Opt. Commun. |

21. | H. Nha and W. Jhe, “Sisyphus cooling on the surface of a hollow-mirror atom trap,” Phys. Rev. A |

22. | J. Yin, Y. Zhu, and Y. Wang, “Gravito-optical trap for cold atoms with doughnut-hollow-beam cooling,” Phys. Lett. A |

23. | I. Manek, Yu. B. Ovchinnikov, and R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Commun. |

24. | D. J. Harris and C. M. Savage, “Atomic gravitational cavities from hollow optical fibers,” Phys. Rev. A |

**OCIS Codes**

(020.1670) Atomic and molecular physics : Coherent optical effects

(020.7010) Atomic and molecular physics : Laser trapping

**ToC Category:**

Research Papers

**History**

Original Manuscript: May 20, 2003

Revised Manuscript: June 28, 2003

Published: August 11, 2003

**Citation**

A. Shevchenko, M. Kaivola, and J. Javanainen, "Heating and phase-space decompression of evanescent-wave cooled atoms by multiple photon reabsorption," Opt. Express **11**, 1827-1834 (2003)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-16-1827

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### References

- J. Söding, R. Grimm, and Yu. B. Ovchinnikov, �??Gravitational laser trap for atoms with evanescent-wave cooling,�?? Opt. Commun. 119, 652-662 (1995). [CrossRef]
- Yu. B. Ovchinnikov, I. Manek, and R. Grimm, �??Surface Trap for Cs atoms based on Evanescent-Wave Cooling,�?? Phys. Rev. Lett. 79, 2225-2228 (1997). [CrossRef]
- M. Hammes, D. Rychtarik, V. Druzhinina, U. Moslener, I. Manek-Hönninger, and R. Grimm, �??Optical and evaporative cooling of caesium atoms in the gravito-optical surface trap,�?? J. Mod. Opt. 47, 2755-2767 (2000).
- P. Desbiolles, M. Arndt, P. Szriftgiser, and J. Dalibard, �??Elementary Sisyphus process close to a dielectric surface,�??Phys. Rev. A 54, 4292-4198 (1996). [CrossRef] [PubMed]
- R. J. C. Spreeuw, D. Voigt, B. T. Wolschrijn, and H. B. van Linden den Heuvell, �??Creating a low-dimensional quantum gas using dark states in an inelastic evanescent-wave mirror,�?? Phys. Rev. A 61, 053604-1-7 (2000). [CrossRef]
- M. Hammes, D. Rychtarik, H.-C. Nägel, and R. Grimm, �??Cold-atom gas at very high densities in an optical surface microtrap,�?? Phys. Rev. A 66, 051401-1-4 (2002). [CrossRef]
- M. Hammes, D. Rychtarik, B. Engeser, H.-C. Nägel, and R. Grimm, �??Evanescent-Wave Trapping and Evaporative Cooling of an Atomic Gas at the Crossover to Two Dimensions,�?? Phys. Rev. Lett. 90, 173001-1-4 (2003). [CrossRef] [PubMed]
- H. Gauck, M. Hartl, D. Schneble, H. Schnitzler, T. Pfau, and J. Mlynek, �??Quasi-2D Gas of Laser Cooled Atoms in a Planar Matter Waveguide,�?? Phys. Rev. Lett. 81, 5298-5301 (1998). [CrossRef]
- P. Domokos and H. Ritsch, �??Efficient laoding and cooling in a dynamic optical evanescent-wave microtrap,�??Europhys. Lett. 54, 306-312 (2001). [CrossRef]
- M. Gorliki, S. Feron, V. Lorent, and M. Dukloy, �??Interferometric approaches to atom-surface van der Waals interactions in atomic mirrors,�?? Phys. Rev. A 61, 013603-1-9 (2000).
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