## Asymmetric superradiant scattering and abnormal mode amplification induced by atomic density distortion |

Optics Express, Vol. 21, Issue 12, pp. 14377-14387 (2013)

http://dx.doi.org/10.1364/OE.21.014377

Acrobat PDF (982 KB)

### Abstract

The superradiant Rayleigh scattering using a pump laser incident along the short axis of a Bose-Einstein condensate with a density distortion is studied, where the distortion is formed by shocking the condensate utilizing the residual magnetic force after the switching-off of the trapping potential. We find that very small variation of the atomic density distribution would induce remarkable asymmetrically populated scattering modes by the matter-wave superradiance with long time pulse. The optical field in the diluter region of the atomic cloud is more greatly amplified, which is not an ordinary mode amplification with the previous cognition. Our numerical simulations with the density envelop distortion are consistent with the experimental results. This supplies a useful method to reflect the geometric symmetries of the atomic density profile by the superradiance scattering.

© 2013 OSA

## 1. Introduction

1. S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, J. Stenger, D. E. Pritchard, and W. Ketterle, “Superradiant Rayleigh scattering from a Bose-Einstein condensate,” Science **285**, 571–574 (1999) [CrossRef] [PubMed] .

9. N. S. Kampel, A. Griesmaier, M. P. Hornbak Steenstrup, F. Kaminski, E. S. Polzik, and J. H. Müller, “The effect of light assisted collisions on matter wave coherence in superradiant Bose-Einstein condensates,” Phys. Rev. Lett. **108**, 090401 (2012) [CrossRef] [PubMed] .

10. A. Hilliard, F. Kaminski, R. le Targat, C. Olausson, E. S. Polzik, and J. H. Müller, “Rayleigh superradiance and dynamic Bragg gratings in an end-pumped Bose-Einstein condensate,” Phys. Rev. A **78**, 051403(R) (2008) [CrossRef] .

11. L. Fallani, C. Fort, N. Piovella, M. Cola, F. S. Cataliotti, M. Inguscio, and R. Bonifacio, “Collective atomic recoil in a moving Bose-Einstein condensate: from superradiance to Bragg scattering,” Phys. Rev. A **71**, 033612 (2005) [CrossRef] .

12. N. Bar-Gill, E. E. Rowen, and N. Davidson, “Spectroscopy of strong-pulse superradiance in a Bose-Einstein condensate,” Phys. Rev. A **76**, 043603 (2007) [CrossRef] .

15. H. Pu, W. Zhang, and P. Meystre, “Wave mixing of optical pulses and Bose-Einstein condensates,” Phys. Rev. lett. **91**, 150407 (2003) [CrossRef] [PubMed] .

16. O. Zobay and G. M. Nikolopoulos, “Spatial effects in superradiant Rayleigh scattering from Bose-Einstein condensates,” Phys. Rev. A **73**, 013620 (2006) [CrossRef] .

6. L. E. Sadler, J. M. Higbie, S. R. Leslie, M. Vengalattore, and D. M. Stamper-Kurn, “Coherence-enhanced imaging of a degenerate Bose-Einstein gas,” Phys. Rev. Lett. **98**, 110401 (2007) [CrossRef] [PubMed] .

17. H. Uys and P. Meystre, “Cooperative scattering of light and atoms in ultracold atomic gases,” Laser Phys. Lett. **5**, 487 (2008) [CrossRef] .

18. L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature **414**, 413–418 (2001) [CrossRef] [PubMed] .

1. S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, J. Stenger, D. E. Pritchard, and W. Ketterle, “Superradiant Rayleigh scattering from a Bose-Einstein condensate,” Science **285**, 571–574 (1999) [CrossRef] [PubMed] .

2. D. Schneble, Y. Torii, M. Boyd, E. W. Streed, D. E. Pritchard, and W. Ketterle, “The onset of matter-wave amplification in a superradiant Bose-Einstein condensate,” Science **300**, 475–478 (2003) [CrossRef] [PubMed] .

13. X. J. Zhou, F. Yang, X. G. Yue, T. Vogt, and X. Z. Chen, “Imprinting light phase on matter-wave gratings in superradiance scattering,” Phys. Rev. A **81**, 013615 (2010) [CrossRef] .

19. B. Lu, X. J. Zhou, T. Vogt, Z. Fang, and X. Z. Chen, “Laser driving of superradiant scattering from a Bose-Einstein condensate at variable incidence angle,” Phys. Rev. A **83**, 033620 (2011) [CrossRef] .

## 2. Experimental description

**k**

*(and frequency*

_{l}*ω*) along its short axis (the

_{l}**x̂**direction), as the typical superradiance scattering demonstrated [1

1. S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, J. Stenger, D. E. Pritchard, and W. Ketterle, “Superradiant Rayleigh scattering from a Bose-Einstein condensate,” Science **285**, 571–574 (1999) [CrossRef] [PubMed] .

2. D. Schneble, Y. Torii, M. Boyd, E. W. Streed, D. E. Pritchard, and W. Ketterle, “The onset of matter-wave amplification in a superradiant Bose-Einstein condensate,” Science **300**, 475–478 (2003) [CrossRef] [PubMed] .

**k**

*} along the longitudinal (the*

_{nm}**ẑ**direction) axis of the condensate. At the same time, the atoms within the condensate will get recoiled to the discrete side-modes (

*n*,

*m*) with momentum

*nh̄*

**k**

*+*

_{l}*mh̄*

**k**

*(*

_{nm}*n*,

*m*are integer). Here, the frequency of the optical fields generated in each end-fire mode shall be different with one another for energy-momentum conservation, depending on the status of the BEC and the experimental configuration. However, one can approximate that

*k*≈

_{nm}*k*≈

_{l}*k*because of the dispersion relation of light. After the superradiant process has been initiated spontaneously, the recoiled atoms would interfere with the condensate, forming a matter-wave grating, and then be amplified by stimulated Rayleigh scattering. At the initial stage, the population of atoms in each recoil side-mode (

*n*,

*m*) grows exponentially following the gain equation [1

**285**, 571–574 (1999) [CrossRef] [PubMed] .

*N*is the atomic number of side-mode (n,m),

_{n,m}*G*and Γ

_{n,m}*are the gain and loss coefficient, respectively, describing the amplification and decoherence of the process.*

_{n,m}*N*= 1.4×10

^{5 87}Rb atoms is prepared in the |

*F*= 2,

*m*= 2〉 hyperfine ground state with a long axis

_{F}*L*= 80

*μm*and short axis

*D*= 8

*μm*in an Ioffe-quadrupole trap with trapping frequencies

*ω*=

_{x}*ω*= 2

_{y}*π*× 220

*Hz*and

*ω*= 2

_{z}*π*× 20

*Hz*. In order to manipulate the atomic density, we shock the condensate by generating a magnetic force via abruptly switching off the trapping potential by the fact that the residual currents remained in the coils of the quadrupole and Ioffe trap decay at different rates. The time control sequence is shown in Fig. 1(b). This results in a BEC with a density profile like that in Fig. 2(a) measured by absorption imaging after free expansion. It can be seen that the density of the BEC is a little higher on the left side. Then after a delay Δ

*t*= 500

*μs*, when the trapping potential has vanished, a laser field with tunable pulse length

*t*and wave length

*λ*= 780

_{l}*nm*, which is red detuned by

*δ*= −0.88

*GHz*to the |

*F*= 2,

*m*= 2〉 → |

_{F}*F′*= 3,

*m*= 3〉 transition, is incident on the condensate along the radial direction to initialize the matter-wave superradiance. The diameter of the pump laser is about 2.2

_{F}*mm*, which is more than 20 times the longitudinal full width at half maximum of the condensate, thus we can treat the laser field as plane wave. Finally, after a 22

*ms*time-of-flight(TOF) for free expansion, the momentum distribution of the matter-wave is measured by absorption imaging.

*I*= 80

*mW/cm*

^{2}and the pulse time

*t*= 100

*μs*. The atomic populations in two first-order forward scattering modes (1, −1) and (1, 1) are measured with the pump beam incident to a BEC before and after the switching-off of the trapping potential, respectively, as shown in the TOF images of the condensate in Figs. 2(b) and 2(c). In the case that the superradiance takes place before the magnetic trap is shut down, the density of a dilute BEC (the interatomic interaction can be neglected in the dilute BEC) is symmetrically distributed within the trap, because the size of the BEC is small compared to the character length scale of the spacial fluctuations of the trapping potential, resulting in a density profile of the Gaussian form symmetric about its geometric center. It is also true that envelop of the BEC should be symmetric even if the condensate is dense. In this situation, the wave-function of the ground state shall take the Thomas-Fermi form in mean-field approximation because of the presence of the atomic interactions. The superradiance of such symmetric BEC has been studied [1

**285**, 571–574 (1999) [CrossRef] [PubMed] .

9. N. S. Kampel, A. Griesmaier, M. P. Hornbak Steenstrup, F. Kaminski, E. S. Polzik, and J. H. Müller, “The effect of light assisted collisions on matter wave coherence in superradiant Bose-Einstein condensates,” Phys. Rev. Lett. **108**, 090401 (2012) [CrossRef] [PubMed] .

## 3. Theoretical model of the density distorted matter-wave Superradiance

16. O. Zobay and G. M. Nikolopoulos, “Spatial effects in superradiant Rayleigh scattering from Bose-Einstein condensates,” Phys. Rev. A **73**, 013620 (2006) [CrossRef] .

*ψ*(

**r**,

*t*) is the atomic wave function.

**E**

^{(±)}are the positive and negative frequency parts of the electric field.

*M*is the atomic mass,

**d**the atomic dipole moment operator,

*ε*

_{0}the vacuum dielectric constant, and

*c*the speed of light in vacuum. Here, the local density distribution of the condensate |

*ψ*(

**r**,

*t*)|

^{2}has to be taken into consideration in Eq. (3) via

**P**

^{(±)}, because the modification of the light fields propagating through the matter-wave grating is prominent in the conditions of the present experimental parameters. In our experiment, the atomic gas is so dilute that the influence from the inter-particle interaction upon the atomic motion is very weak. Therefore, the nonlinear matter-wave self interacting term is not included in this equation, and the atomic loss term resulted from the nonlinear effects in the time scales of our experiment should also be negligible [4

4. Y. Yoshikawa, Y. Torii, and T. Kuga, “Superradiant light scattering from thermal atomic vapors,” Phys. Rev. Lett. **94**, 083602 (2005) [CrossRef] [PubMed] .

6. L. E. Sadler, J. M. Higbie, S. R. Leslie, M. Vengalattore, and D. M. Stamper-Kurn, “Coherence-enhanced imaging of a degenerate Bose-Einstein gas,” Phys. Rev. Lett. **98**, 110401 (2007) [CrossRef] [PubMed] .

9. N. S. Kampel, A. Griesmaier, M. P. Hornbak Steenstrup, F. Kaminski, E. S. Polzik, and J. H. Müller, “The effect of light assisted collisions on matter wave coherence in superradiant Bose-Einstein condensates,” Phys. Rev. Lett. **108**, 090401 (2012) [CrossRef] [PubMed] .

*F*=

*πD*

^{2}/(4

*λ*) of the optical pump field in our experiment is around 1, so that we can using the quasi-2D model to investigate the dynamics of the condensate in the superradiant processes. In our experiment, the atomic gas is dilute, thus one can decompose the atomic wave function in the discrete modes [16

_{l}L16. O. Zobay and G. M. Nikolopoulos, “Spatial effects in superradiant Rayleigh scattering from Bose-Einstein condensates,” Phys. Rev. A **73**, 013620 (2006) [CrossRef] .

*ψ*represents the wave function of the side-mode (

_{n,m}*n*,

*m*), and

*h̄ω*= (

_{nm}*n*

^{2}+

*m*

^{2})

*h̄ω*is the kinetic energy of one single atom in this mode with

_{r}*A*is the effective cross section area of the condensate. In the case of an symmetric BEC,

*A*should be constant. Atomic number in the (n,m) mode can be calculated as Similarly to the discrete expansion of the matter-wave function, the optical fields can be expressed in the form of running wave with few frequency components, because the band width of the laser beam is very narrow, where

*ε*,

_{l}*ε*

_{±}are the envelope functions of the pump laser and the end-fire modes, respectively (+ corresponds to the end-fire mode propagating along the positive

*z*direction, and − represents that in the opposite direction).

**e**

*is the unit polarization vector of the electric field along the*

_{y}*y*direction.

*τ*= 2

*ω*, and

_{r}t*ξ*=

*kz*, Eq. (2) can be recast to the following dimensionless form,

*e*

_{±}of the end-fire modes in the dimensionless form are given by with

*e*

_{+}is taken from −∞ to

*ξ*, while that for

*e*

_{−}is taken from

*ξ*to ∞.

*v*

_{0}. In a typical matter-wave interference experiment, the interference patterns of the scattered matter-wave is sensitively dependent on the local phase and density distributions of the condensate. However, we find that, in our situation, the local phase imprinted upon the condensate by the atomic acceleration has little influence upon the dynamics of the condensate (for making good consistency of the different parts of the paper, the detailed analysis of the influence upon the atomic motion from the acceleration is presented in the Appendix). In drastic contrast, even a tiny disturbance of atomic density distribution would generate prominent asymmetric interference patterns of the scattered matter-wave in the superradiant process. This makes our experiment a rather robust technique for measuring the geometric symmetry of BECs with high precision.

## 4. The density modulation analysis and numerical simulation

*κ*in Eq. (7) via the

*z*-dependence of the effective cross section area of the condensate

*A*. To describe such a mechanism that the atomic density distortion modifies the matter-wave superradiance, we multiply a factor

*S*

^{−2}(

*z*) to the effective cross section area of the condensate

*A*→

*A/S*

^{2}(

*z*). In the regime where the distortion is very weak,

*S*(

*z*) can be approximated up to the linear order of

*z*,

*l*that should be fitted from the experimental data. During the radial expansion, the atomic number

*N*(

*z*) = |

*ψ*

_{00}(

*z*)|

^{2}will not change, thus the asymmetric cross section

*A/S*

^{2}(

*z*) would lead to a transformation of the coupling constant

*κ*→

*κ*(1 +

*ξ*/Λ) with Λ =

*kl*. The envelope of the density distribution of the initial distorted condensate

*ψ*used in our simulation is shown in Fig. 3(a). It is a modified function in Thomas-Fermi approximation

*ψ*(

_{s}*z*)|

^{2}= 3/4

*L*

^{3}[(

*L*/2)

^{2}−

*z*

^{2}]Θ(

*L*/2 − |

*z*|) with Θ(

*z*) the Heaviside step function.

*ψ*is a seed wave function indicating one atom in a side-mode. To measure the asymmetry of the initial BEC, we define a parameter

_{s}*dz*in describing the displacement of the peak density point of the condensate from its geometric center. In our simulation,

*dz*= 3.16

*μm*. This tiny shift is hardly measurable in ordinary imaging system. However, by monitoring the symmetry of the dynamics of the scattered matter-wave in the superradiant process, one can obtain information of the geometric symmetry of the condensate, which is exclusively available in using the

*in situ*imaging methods [20

20. M. R. Andrews, M.-O. Mewes, N. J. Druten, and D. S. Durfee, Direct, “Nondestructive observation of a Bose condensate,” Science **273**, 84–87 (1996) [CrossRef] [PubMed] .

21. N. Gemelke, X. Zhang, C. L. Hung, and C. Chin, “In situ observation of incompressible Mott-insulating domains in ultracold atomic gases,” Nature **460**, 995–998 (2009) [CrossRef] [PubMed] .

### 4.1. Early stage

*ψ*

_{00}and

*ψ*

_{1,±1}by the electric field

*e*

_{±}, respectively.

*τ*→ 0, the first two kinetic terms in Eq. (9) are negligible, leading to an exact expression of the atomic population in each side-mode as, with The integrals in Eqs. (12) and (13) can be numerically carried out to give in the dimension-less notion

*G*

_{1,1}= 16.7 and

*G*

_{1,−1}= 15.9, implying that the atomic populations in these two side-modes increase exponentially at the beginning of the matter-wave superradiant process as shown in the experimental data and numerical simulation in Fig. 3(b). Even though such growing is unbalanced for the (1, ±1) modes, the asymmetry of the matter-wave superradiance is hardly visible in experiment in this limit, because the atomic populations in these two modes are too small. However, the numerical simulation is consistent with the experimental data in predicting the exponential growing of the atomic numbers in the side-modes in this stage.

### 4.2. Long pulse regime

*l*= −500

*μm*. To fit the experimental result with the quasi-two dimensional model, the numerical result is scaled by a factor of 2. This discrepancy is partly due to the collision between the side-modes and the condensate [12

12. N. Bar-Gill, E. E. Rowen, and N. Davidson, “Spectroscopy of strong-pulse superradiance in a Bose-Einstein condensate,” Phys. Rev. A **76**, 043603 (2007) [CrossRef] .

22. N. Katz, J. Steinhauer, R. Ozeri, and N. Davidson, “Beliaev damping of quasiparticles in a Bose-Einstein condensate,” Phys. Rev. Lett. **89**, 220401 (2002) [CrossRef] [PubMed] .

23. P. R. Berman, “Comparison of recoil-induced resonances and the collective atomic recoil laser,” Phys. Rev. A **59**, 585 (1999) [CrossRef] .

*t*= 500

*μs*in our experiment, the condensate is shocked and distorted by the residual magnetic force to take the shape like that in Fig. 2(a). The matter-wave superradiance shows unconventional mode amplification behaviors. It is seen in Fig. 3(c) that, the

*ε*

_{+}and

*ε*

_{−}end-fire modes are mainly amplified and concentrated in the right part and left part of the condensate, respectively, and the condensate here functions as the gain medium for the optical mode amplification. However, for longer pulse durations, even though the density in the left side of the condensate is higher than that in the left side, the (1, −1) mode grows faster than the (1, 1) mode, implying that

*ε*

_{+}end-fire mode is more quickly amplified than that propagating in the opposite direction. This is in contradiction with our common cognition that the optical mode should be better amplified provided that the gain medium is denser.

*z*< 0) of the condensate is denser than that in the right part, making the

*e*

_{+}mode grow faster than the

*e*

_{−}mode. In fact, the faster growing of

*e*

_{+}in the central region is true in the full range of the pulse duration, including the early stage of the process, as shown in Figs. 3(b) and 3(c). This makes the wave function of the (1, −1) mode have a fatter tail than that of the (1, 1) mode (see in Fig.3(c)) in the central region of the condensate, leading to a greater overlap for (1, −1) with (0, 0) source mode. This makes the coupling between the (1, −1) and (0, 0) modes stronger than that for the (1, 1) and (0, 0) modes. Therefore, for long pulse durations, there are more atoms being scattered to (1, −1) mode by the

*e*

_{+}light, leading to a higher atomic population in the (1, −1) side-mode. This phenomenon has been observed in the experiment as shown in Fig. 3(b).

*t*= 120

*μs*, there has been a considerable number of atoms that are excited to the (2, 0) mode. The pump laser, together with the light fields in all the end-fire modes, couples the different atomic side-modes with each other. This makes the atomic superradiance a process rather like the atomic Bragg diffraction. Besides the fact that the (1, −1) mode is stronger than the (1, 1) mode, the atomic population in each side-mode begins to oscillate in the time domain.

## 5. Conclusion

## Appendix A. The influence from the atomic acceleration

*v*

_{0}in the positive

*z*direction. However, by changing the reference frame to the one moving with the condensate, it can be find that Eq. (7) is invariant under such a Galilean transformation. In fact, the pump laser together with each of the generated end-fire modes (with wave vector

**k**

_{±}and frequency

*ω*

_{±}) creates a pair of moving optical lattices with intensity

*I*

_{±}(

**r**,

*t*) ∝

*cos*(

**q**

_{±}·

**r**− Δ

*ω*

_{±}

*t*) as shown in Fig. 4, in which

**q**

_{±}=

**k**

*−*

_{l}**k**

_{±}, Δ

*ω*

_{±}=

*ω*−

_{l}*ω*

_{±}. In stationary case, i.e.,

*v*

_{0}= 0, we have

*ω*

_{+}=

*ω*

_{−}, and the speeds of these optical lattices are both

**ẑ**direction at a speed 2

*ω*/

_{r}*k*.

*v*

_{0}= 2

*ω*, where

_{r}m′/k*m′*can be fractional, the frequency of each of the scattered light will have a Doppler shift, leading to the modification, and resulting in a new sets of lattices with modified speed

*v′*

_{±}= 2

*ω*(∓1+

_{r}*m′*) in

**ẑ**direction, i.e., compared to the stationary case, the speed of the generated optical lattices are both increased by 2

*ω*, which is exactly the same as

_{r}m′/k*v*

_{0}. In other words, the matter-wave superradiance of a moving condensate is equivalent with performing the superradiant experiment of a stationary BEC in a moving laboratory. Therefore, the atomic acceleration will induce no asymmetries in the atomic dynamics in the matter-wave superradiant processes.

*e*(where,

^{i(k′x−ω′t)}## Acknowledgments

## References and links

1. | S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, J. Stenger, D. E. Pritchard, and W. Ketterle, “Superradiant Rayleigh scattering from a Bose-Einstein condensate,” Science |

2. | D. Schneble, Y. Torii, M. Boyd, E. W. Streed, D. E. Pritchard, and W. Ketterle, “The onset of matter-wave amplification in a superradiant Bose-Einstein condensate,” Science |

3. | M. Kozuma, Y. Suzuki, Y. Torii, T. Sugiura, T. Kuga, E. W. Hagley, and L. Deng, “Phase-coherent amplipcation of matter waves,” Science |

4. | Y. Yoshikawa, Y. Torii, and T. Kuga, “Superradiant light scattering from thermal atomic vapors,” Phys. Rev. Lett. |

5. | Y. Yoshikawa, K. Nakayama, Y. Torii, and T. Kuga, “Holographic storage of multiple coherence gratings in a Bose-Einstein condensate,” Phys. Rev. Lett. |

6. | L. E. Sadler, J. M. Higbie, S. R. Leslie, M. Vengalattore, and D. M. Stamper-Kurn, “Coherence-enhanced imaging of a degenerate Bose-Einstein gas,” Phys. Rev. Lett. |

7. | F. Yang, X. J. Zhou, J. T. Li, Y. K Chen, L. Xia, and X. Z. Chen, “Resonant sequential scattering in two-frequency-pumping superradiance from a Bose-Einstein condensate,” Phys. Rev. A |

8. | L. Deng, E. W. Hagley, Q. Cao, X. Wang, X. Luo, R. Wang, M. G. Payne, F. Yang, X. Zhou, X. Chen, and M. Zhan, “Observation of a red-blue detuning asymmetry in matter-wave superradiance,” Phys. Rev. Lett. |

9. | N. S. Kampel, A. Griesmaier, M. P. Hornbak Steenstrup, F. Kaminski, E. S. Polzik, and J. H. Müller, “The effect of light assisted collisions on matter wave coherence in superradiant Bose-Einstein condensates,” Phys. Rev. Lett. |

10. | A. Hilliard, F. Kaminski, R. le Targat, C. Olausson, E. S. Polzik, and J. H. Müller, “Rayleigh superradiance and dynamic Bragg gratings in an end-pumped Bose-Einstein condensate,” Phys. Rev. A |

11. | L. Fallani, C. Fort, N. Piovella, M. Cola, F. S. Cataliotti, M. Inguscio, and R. Bonifacio, “Collective atomic recoil in a moving Bose-Einstein condensate: from superradiance to Bragg scattering,” Phys. Rev. A |

12. | N. Bar-Gill, E. E. Rowen, and N. Davidson, “Spectroscopy of strong-pulse superradiance in a Bose-Einstein condensate,” Phys. Rev. A |

13. | X. J. Zhou, F. Yang, X. G. Yue, T. Vogt, and X. Z. Chen, “Imprinting light phase on matter-wave gratings in superradiance scattering,” Phys. Rev. A |

14. | M. G. Moore and P. Meystre, “Theory of superradiant scattering of laser light from Bose-Einstein condensates,” Phys. Rev. lett. |

15. | H. Pu, W. Zhang, and P. Meystre, “Wave mixing of optical pulses and Bose-Einstein condensates,” Phys. Rev. lett. |

16. | O. Zobay and G. M. Nikolopoulos, “Spatial effects in superradiant Rayleigh scattering from Bose-Einstein condensates,” Phys. Rev. A |

17. | H. Uys and P. Meystre, “Cooperative scattering of light and atoms in ultracold atomic gases,” Laser Phys. Lett. |

18. | L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature |

19. | B. Lu, X. J. Zhou, T. Vogt, Z. Fang, and X. Z. Chen, “Laser driving of superradiant scattering from a Bose-Einstein condensate at variable incidence angle,” Phys. Rev. A |

20. | M. R. Andrews, M.-O. Mewes, N. J. Druten, and D. S. Durfee, Direct, “Nondestructive observation of a Bose condensate,” Science |

21. | N. Gemelke, X. Zhang, C. L. Hung, and C. Chin, “In situ observation of incompressible Mott-insulating domains in ultracold atomic gases,” Nature |

22. | N. Katz, J. Steinhauer, R. Ozeri, and N. Davidson, “Beliaev damping of quasiparticles in a Bose-Einstein condensate,” Phys. Rev. Lett. |

23. | P. R. Berman, “Comparison of recoil-induced resonances and the collective atomic recoil laser,” Phys. Rev. A |

**OCIS Codes**

(270.6630) Quantum optics : Superradiance, superfluorescence

(290.5870) Scattering : Scattering, Rayleigh

(020.1475) Atomic and molecular physics : Bose-Einstein condensates

**ToC Category:**

Atomic and Molecular Physics

**History**

Original Manuscript: April 8, 2013

Revised Manuscript: May 24, 2013

Manuscript Accepted: May 25, 2013

Published: June 10, 2013

**Citation**

Zhongkai Wang, Linxiao Niu, Peng Zhang, Mingxuan Wen, Zhen Fang, Xuzong Chen, and Xiaoji Zhou, "Asymmetric superradiant scattering and abnormal mode amplification induced by atomic density distortion," Opt. Express **21**, 14377-14387 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-12-14377

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### References

- S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, J. Stenger, D. E. Pritchard, and W. Ketterle, “Superradiant Rayleigh scattering from a Bose-Einstein condensate,” Science285, 571–574 (1999). [CrossRef] [PubMed]
- D. Schneble, Y. Torii, M. Boyd, E. W. Streed, D. E. Pritchard, and W. Ketterle, “The onset of matter-wave amplification in a superradiant Bose-Einstein condensate,” Science300, 475–478 (2003). [CrossRef] [PubMed]
- M. Kozuma, Y. Suzuki, Y. Torii, T. Sugiura, T. Kuga, E. W. Hagley, and L. Deng, “Phase-coherent amplipcation of matter waves,” Science286, 2309–2312 (1999). [CrossRef] [PubMed]
- Y. Yoshikawa, Y. Torii, and T. Kuga, “Superradiant light scattering from thermal atomic vapors,” Phys. Rev. Lett.94, 083602 (2005). [CrossRef] [PubMed]
- Y. Yoshikawa, K. Nakayama, Y. Torii, and T. Kuga, “Holographic storage of multiple coherence gratings in a Bose-Einstein condensate,” Phys. Rev. Lett.99, 220407 (2007). [CrossRef]
- L. E. Sadler, J. M. Higbie, S. R. Leslie, M. Vengalattore, and D. M. Stamper-Kurn, “Coherence-enhanced imaging of a degenerate Bose-Einstein gas,” Phys. Rev. Lett.98, 110401 (2007). [CrossRef] [PubMed]
- F. Yang, X. J. Zhou, J. T. Li, Y. K Chen, L. Xia, and X. Z. Chen, “Resonant sequential scattering in two-frequency-pumping superradiance from a Bose-Einstein condensate,” Phys. Rev. A78, 043611 (2008). [CrossRef]
- L. Deng, E. W. Hagley, Q. Cao, X. Wang, X. Luo, R. Wang, M. G. Payne, F. Yang, X. Zhou, X. Chen, and M. Zhan, “Observation of a red-blue detuning asymmetry in matter-wave superradiance,” Phys. Rev. Lett.105, 220404 (2010). [CrossRef]
- N. S. Kampel, A. Griesmaier, M. P. Hornbak Steenstrup, F. Kaminski, E. S. Polzik, and J. H. Müller, “The effect of light assisted collisions on matter wave coherence in superradiant Bose-Einstein condensates,” Phys. Rev. Lett.108, 090401 (2012). [CrossRef] [PubMed]
- A. Hilliard, F. Kaminski, R. le Targat, C. Olausson, E. S. Polzik, and J. H. Müller, “Rayleigh superradiance and dynamic Bragg gratings in an end-pumped Bose-Einstein condensate,” Phys. Rev. A78, 051403(R) (2008). [CrossRef]
- L. Fallani, C. Fort, N. Piovella, M. Cola, F. S. Cataliotti, M. Inguscio, and R. Bonifacio, “Collective atomic recoil in a moving Bose-Einstein condensate: from superradiance to Bragg scattering,” Phys. Rev. A71, 033612 (2005). [CrossRef]
- N. Bar-Gill, E. E. Rowen, and N. Davidson, “Spectroscopy of strong-pulse superradiance in a Bose-Einstein condensate,” Phys. Rev. A76, 043603 (2007). [CrossRef]
- X. J. Zhou, F. Yang, X. G. Yue, T. Vogt, and X. Z. Chen, “Imprinting light phase on matter-wave gratings in superradiance scattering,” Phys. Rev. A81, 013615 (2010). [CrossRef]
- M. G. Moore and P. Meystre, “Theory of superradiant scattering of laser light from Bose-Einstein condensates,” Phys. Rev. lett.83, 5202–5205 (1999). [CrossRef]
- H. Pu, W. Zhang, and P. Meystre, “Wave mixing of optical pulses and Bose-Einstein condensates,” Phys. Rev. lett.91, 150407 (2003). [CrossRef] [PubMed]
- O. Zobay and G. M. Nikolopoulos, “Spatial effects in superradiant Rayleigh scattering from Bose-Einstein condensates,” Phys. Rev. A73, 013620 (2006). [CrossRef]
- H. Uys and P. Meystre, “Cooperative scattering of light and atoms in ultracold atomic gases,” Laser Phys. Lett.5, 487 (2008). [CrossRef]
- L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature414, 413–418 (2001). [CrossRef] [PubMed]
- B. Lu, X. J. Zhou, T. Vogt, Z. Fang, and X. Z. Chen, “Laser driving of superradiant scattering from a Bose-Einstein condensate at variable incidence angle,” Phys. Rev. A83, 033620 (2011). [CrossRef]
- M. R. Andrews, M.-O. Mewes, N. J. Druten, and D. S. Durfee, Direct, “Nondestructive observation of a Bose condensate,” Science273, 84–87 (1996). [CrossRef] [PubMed]
- N. Gemelke, X. Zhang, C. L. Hung, and C. Chin, “In situ observation of incompressible Mott-insulating domains in ultracold atomic gases,” Nature460, 995–998 (2009). [CrossRef] [PubMed]
- N. Katz, J. Steinhauer, R. Ozeri, and N. Davidson, “Beliaev damping of quasiparticles in a Bose-Einstein condensate,” Phys. Rev. Lett.89, 220401 (2002). [CrossRef] [PubMed]
- P. R. Berman, “Comparison of recoil-induced resonances and the collective atomic recoil laser,” Phys. Rev. A59, 585 (1999). [CrossRef]

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