Raman amplification of matter waves

Schneble, Dominik; Campbell, Gretchen K.; Streed, Erik; Boyd, Martin M.; Pritchard, David E.; Ketterle, Wolfgang

doi:10.1103/physreva.69.041601

Cited by 82 publications

(112 citation statements)

References 17 publications

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“…In these experiments, the atoms after the collective scattering remain in the original internal, gaining a recoil momentum h( k 2 − k 1 ), where k 2 and k 1 are the wave vectors of the pump and scattered photons, respectively. The scattered atoms may experience further collective scattering, leading to the observed superradiant cascade [6].In two recent experiments [10,11] it has been observed superradiant Raman scattering, in which the atoms remain, after the process, in a different hyperfine state not resonant with the pump laser beam. As a consequence, no further scattering of pump photons occurs.…”

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confidence: 99%

“…In two recent experiments [10,11] it has been observed superradiant Raman scattering, in which the atoms remain, after the process, in a different hyperfine state not resonant with the pump laser beam. As a consequence, no further scattering of pump photons occurs.…”

mentioning

confidence: 99%

“…[10], a cigar-shaped 87 Rb condensate was illuminated with single laser beam π polarized and detuned by ∆ 2 /(2π) = −340 MHz from the D 2 line transition (λ = 780 nm), between |b = |5 2 S 1/2 , F = 1, m F = 1 and |e = |5 2 P 3/2 , F = 1, m F = 1 . After emission of a photon σ + polarized in the end-fire mode of the condensate, the atoms return to the ground state |c = |5 2 S 1/2 , F = 2, m F = 2 , recoiling at an angle of 45 0 with momentum p =h q.…”

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confidence: 99%

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Theory of collective Raman scattering from a Bose-Einstein condensate

Cola

Piovella

2004

Phys. Rev. A

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Recent experiments have demonstrated superradiant Raman scattering from a Bose-Einstein condensate driven by a single off-resonant laser beam. We present a quantum theory describing this phenomenon, showing Raman amplification of matter wave due to collective atomic recoil from 3-level atoms in a Λ-configuration. When atoms are initially in a single lower internal state, a closed two-level system is realized between atoms with different internal states, and entangled atom-photon pairs can be generated. When atoms are initially prepared in both the lower internal states, a fraction of atoms recoiling in the backward direction can be generated.PACS numbers: 42.50.Fx, 42.50.Vk, 42.65.Dr Important progress in the study of the coherent interaction between atoms and photons have been recently obtained using Bose-Einstein condensates (BEC) of low-density alkali atoms [1]. In the case where the atoms interact only with far off-resonant optical fields, the dominant atom-photon interaction is two-photon Rayleigh scattering. In this situation, collective atomic recoil lasing (CARL) [2,3,4,5] causes exponential enhancement of the number of scattered photons and atoms. Experimentally, CARL from a BEC has been observed so far in the Superradiant regime [6,7,8,9], in which photons are scattered into the end-fire modes along the major axis of an elongated condensate. In these experiments, the atoms after the collective scattering remain in the original internal, gaining a recoil momentum h( k 2 − k 1 ), where k 2 and k 1 are the wave vectors of the pump and scattered photons, respectively. The scattered atoms may experience further collective scattering, leading to the observed superradiant cascade [6].In two recent experiments [10,11] it has been observed superradiant Raman scattering, in which the atoms remain, after the process, in a different hyperfine state not resonant with the pump laser beam. As a consequence, no further scattering of pump photons occurs. In this Brief Report, we present a theory of the collective atomic recoil lasing from a 3-level atomic BEC which describes the observed phenomena. In particular, the theory demonstrates that maximum atom-photon entanglement can be generated in this system.We consider a cloud of BEC atoms which have three internal states labeled by |b , |c , and |e with energies E b < E c < E e , respectively. The two lower states |b and |c can be hyperfine states in each of which the atoms can live for a long time. They are coupled to the upper state |e via, respectively, a classical pump field and a quantized probe field of frequencies ω 2 and ω 1 in the Λ-configuration. The interaction scheme is shown in Fig. 1.The second quantized Hamiltonian to describe the system at zero temperature is given bŷwhereĤ atom gives the free evolution of the the atomic fields andĤ atom−f ield describes the dipole interactions between the atomic fields and the pump and probe fields. We assume the condensate to be sufficiently diluite in order to neglect the atom-atom interaction. The free atomic Hami...

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confidence: 99%

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Theory of collective Raman scattering from a Bose-Einstein condensate

Cola

Piovella

2004

Phys. Rev. A

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“…superradiance transition [15][16][17][18][19][20][21], in which the initial population ofÊ 2 is set to zero, and the population transfer between j1i and j2i is driven by the absorption of a photon fromÊ 1 , and the spontaneous emission of a photon intoÊ 2 . A small ''seed'' of atoms in j2i, which could be populated via a conventional Raman transition, stimulates the transfer such that the majority of photons are emitted into a single mode.…”

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Information-Recycling Beam Splitters for Quantum Enhanced Atom Interferometry

Haine

2013

Phys. Rev. Lett.

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We propose a scheme to significantly enhance the sensitivity of atom interferometry performed with Bose-Einstein condensates. When an optical two-photon Raman transition is used to split the condensate into two modes, some information about the number of atoms in one of the modes is contained in one of the optical modes. We introduce a simple model to describe this process, and find that by processing this information in an appropriate way, the phase sensitivity of atom interferometry can be enhanced by more than a factor of 10 for realistic parameters.

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“…The third approach is to use an elongated atomic cloud, in which the optical modes along the long axis of the cloud (referred to as "end-fire modes") have automatically large N η [13]. This system has been recently investigated in the context of superradiant light scattering from BoseEinstein condensates (BECs) [14,15,16,17]. Note that, in the second and the third approach, the spatial modes possessing large N η are independent of the pump-beam direction, then allowing simultaneous writing of many coherence gratings in the single cloud.…”

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Holographic Storage of Multiple Coherence Gratings in a Bose-Einstein Condensate

et al. 2007

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We demonstrate superradiant conversion between a two-mode collective atomic state and a singlemode light field in an elongated cloud of Bose-condensed atoms. Two off-resonant write beams induce superradiant Raman scattering, producing two independent coherence gratings with different wave vectors in the cloud. By applying phase-matched read beams after a controllable delay, the gratings can be selectively converted into the light field also in a superradiant way. Due to the large optical density and the small velocity width of the condensate, a high conversion efficiency of > 70 % and a long storage time of > 120 µs were achieved.PACS numbers: 42.50.Gy Atomic ensemble is a promising candidate for quantum memory, in which quantum information can be stored as a long-lived ground-state coherence. In contrast, photons are ideal for long-distance quantum-state transfer since they travel fast and are robust against perturbations from environment. The conversion of quantum states between atoms and photons has thus been an important subject in recent years [1,2,3,4,5,6,7,8,9,10,11]. In particular, on the basis of spontaneous Raman scattering and coherent reverse processes [1,2], various applications, including generation of single photons [3,4,5], correlated photon pairs [6,7,8] and entangled states [9,10], have been successfully demonstrated.In general, indistinguishable atoms interacting with a single-mode light field shows enhanced light scattering by a factor of N , where N is the number of atoms. This cooperative effect is the key factor for the efficient conversion from an atomic coherence to the light field in a well-defined spatial mode [1,11]. The figure of merit is given by the optical density of atoms along the mode axis N η, where η ≡ σ a /A is the single-atom optical density. Here σ a is the atomic absorption cross section and A is the cross section of the interaction region perpendicular to the mode axis. In free space η is scaled as the solid angle determined by the diffraction of scattered photons ≈ λ 2 /D 2 , with the light wavelength λ and the cloud diameter D. Therefore, N η roughly gives R m /R, the ratio of the photon scattering rate into the desired mode R m to that into the other mode R. The conversion efficiency can then be written asTo achieve large N η, the most popular method is to use forward Raman scattering from an elongated interaction volume, determined by the pump-beam path in the atomic ensemble [1,3,4,6,7,8,9,10]. An alternative approach is to put the atoms into an optical cavity [5], where the photon emission into the cavity mode is enhanced by the Purcell factor ≈ 2ζN η, where ζ is the number of round trips of photons in the cavity [12]. The third approach is to use an elongated atomic cloud, in which the optical modes along the long axis of the cloud (referred to as "end-fire modes") have automatically large N η [13]. This system has been recently investigated in the context of superradiant light scattering from BoseEinstein condensates (BECs) [14,15,16,17]. Note that, in the se...

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Raman amplification of matter waves

Cited by 82 publications

References 17 publications

Theory of collective Raman scattering from a Bose-Einstein condensate

Theory of collective Raman scattering from a Bose-Einstein condensate

Information-Recycling Beam Splitters for Quantum Enhanced Atom Interferometry

Holographic Storage of Multiple Coherence Gratings in a Bose-Einstein Condensate

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