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arXiv:1204.4682 · New Journal of Physics

Bragg spectroscopic interferometer and quantum measurement-induced correlations in atomic Bose–Einstein condensates

M D Lee, Stefan Rist, Janne Ruostekoski

Published Jul 31, 2012• 5 citations
arXivHTMLPDF

Abstract

We theoretically analyse the Bragg spectroscopic interferometer of two spatially separated atomic Bose–Einstein condensates that was experimentally realized by Saba et al (2005 Science 307 1945) by continuously monitoring the relative phase evolution. Even though atoms in the light-stimulated Bragg scattering interact with intense coherent laser beams, we show that the phase is created by quantum measurement-induced backaction on the homodyne photocurrent of the lasers, opening the possibilities for quantum-enhanced interferometric schemes. We identify two regimes of phase evolution: a running phase regime observed in the experiment of Saba et al , which is sensitive to an energy offset and suitable for an interferometer, and a trapped phase regime, which can be insensitive to the applied forces and detrimental to interferometric applications.

DOI
10.1088/1367-2630/14/7/073057

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•Jan 1, 2011•0 citations
We theoretically analyse the Bragg spectroscopic interferometer of two spatially separated atomic Bose–Einstein condensates that was experimentally realized by Saba et al (2005 Science 307 1945) by continuously monitoring the relative phase evolution. Even though atoms in the light-stimulated Bragg scattering interact with intense coherent laser beams, we show that the phase is created by quantum measurement-induced backaction on the homodyne photocurrent of the lasers, opening the possibilities for quantum-enhanced interferometric schemes. We identify two regimes of phase evolution: a running phase regime observed in the experiment of Saba et al , which is sensitive to an energy offset and suitable for an interferometer, and a trapped phase regime, which can be insensitive to the applied forces and detrimental to interferometric applications.
We demonstrated an experimental technique based on stimulated light scattering to continuously sample the relative phase of two spatially separated Bose-Einstein condensates of atoms. The phase measurement process created a relative phase between two condensates with no initial phase relation, read out the phase, and monitored the phase evolution. This technique was used to realize interferometry between two trapped Bose-Einstein condensates without need for splitting or recombining the atom cloud.
We propose a scheme for trapped-atom interferometry using an interacting Bose-Einstein condensate. The condensate is controlled and spatially split into two confined external momentum modes through a series of Bragg pulses. The proposed scheme (i) allows the generation of large entanglement in a trapped-interferometer configuration via one-axis twisting dynamics induced by interatomic interaction and (ii) avoids the suppression of interactions during the interferometer sequence by a careful manipulation of the state before and after phase encoding. The interferometer can be used for the measurement of gravity with a sensitivity beyond the standard quantum limit.
Bose–Einstein condensates of particles behave in many ways like coherent radiation fields, and the realization of Bose–Einstein condensation in dilute gases has opened up the experimental study of many aspects of interactions between coherent matter waves. In addition, the existence of these dilute trapped quantum gases has prompted a re-examination of a number of theoretical issues. This field is a vast one, and in this chapter we shall touch briefly on selected topics. In Sec. 13.1 we describe the classic interference experiment, in which two clouds of atoms are allowed to expand and overlap. Rather surprisingly, an interference pattern is produced even though initially the two clouds are completely isolated. We shall analyse the reasons for this effect. The marked decrease in density fluctuations in a Bose gas when it undergoes Bose–Einstein condensation is demonstrated in Sec. 13.2. Gaseous Bose–Einstein condensates can be manipulated by lasers, and this has made possible the study of coherent matter wave optics. We describe applications of these techniques to observe solitons, Bragg scattering, and non-linear mixing of matter waves in Sec. 13.3. The atom laser and amplification of matter waves is taken up in Sec. 13.4. How to characterize Bose–Einstein condensation microscopically is the subject of Sec. 13.5, where we also consider fragmented condensates. Interference of two condensates One of the striking manifestations of the wave nature of Bose–Einstein condensates is the observation of an interference pattern when two condensed and initially separated clouds are allowed to overlap. An example is shown in Fig. 13.1.
We propose an experiment for entangling two spatially separated Bose-Einstein condensates by Bragg scattering of light. When Bragg scattering in two condensates is stimulated by a common probe, the resulting quasiparticles or particles in the two condensates get entangled due to quantum communication between the condensates via the probe beam. The entanglement is shown to be significant and occurs in both number and quadrature phase variables and depends strongly on the relative detuning of the two pumps and the relative atom-field coupling strengths of the two condensates. We present two methods of detecting the generated entanglement.
Bose–Einstein condensates of particles behave in many ways like coherent radiation fields, and the realization of Bose–Einstein condensation in dilute gases has opened up the experimental study of interactions between coherent matter waves. In addition, the existence of these dilute trapped quantum gases has prompted a re-examination of a number of theoretical issues. In Sec. 13.1 we discuss Josephson tunnelling of a condensate between two wells and the role of fluctuations in particle number and phase. The number and phase variables play a key role in the description of the classic interference experiment, in which two clouds of atoms are allowed to expand and overlap (Sec. 13.2). Rather surprisingly, an interference pattern is produced even though initially the two clouds are completely isolated. Density fluctuations in a Bose gas are studied in Sec. 13.3, where we relate atomic clock shifts to the two-particle correlation function. The ability to manipulate gaseous Bose–Einstein condensates by lasers has made possible the study of coherent matter wave optics and in Sec. 13.4 we describe applications of these techniques to observe solitons, Bragg scattering, and non-linear mixing of matter waves. How to characterize Bose–Einstein condensation in terms of the density matrix is the subject of Sec. 13.5, where we also consider fragmented condensates.
Bose-Einstein condensates are coherent matter waves, produced by cooling gaseous atomic clouds to ultra-low temperatures. For applications in atom interferometry and precision measurements, Bose-condensed sources present an intriguing alternative to thermal atoms. Although the current sensitivity achievable with interferometers using coherent atoms is not comparable to thermal beam machines (mainly due to the lower flux), there are promising ways to utilise the potential of Bose-condensed sources for atom interferometry. Among those is the low momentum width of Bose-Einstein condensates, which can generally be well controlled and is advantageous for increased interferometric sensitivities by implementing large momentum transfer beam splitters. As part of this thesis, experimental and theoretical investigations are presented to investigate the potential of Bose-Einstein condensates for such applications. We shall present the quantum projection noise limited performance of a Ramsey interferometer operating on the atomic clock transition of a freely expanding cloud of Bose-condensed rubidium 87 atoms. The results include Ramsey fringes of high visibility, not measurably affected by atomic interaction-induced dephasing effects. The achievement and detection of the quantum projection noise limit rely critically on the precision and accuracy of both the imaging setup and the coupling scheme in the interferometric beam splitters. The stabilisation of the beam splitters via an optical Sagnac interferometer is the basis for the quantum projection noise limited performance of the interferometer presented. For an increase of bandwidth and flux in atom interferometric measurements, it is advantageous to use a continuous atomic beam. A truly continuous coherent atom source has not been realised to date, and we present results on a pumping mechanism in this thesis, as a decisive step towards a continuous atom laser. By the investigation of different momentum resonances, we find that the pumping scheme relies on a Raman superradiance-like process. Finally, the thesis demonstrates two interaction measurements in rubidium. The strong mean field interactions due to the high densities in Bose-Einstein condensates are used to probe the potential of a rubidium 87 condensate with an atom laser. The measurement allows a determination of the scattering length between the two atomic states involved. In addition to this two-body scattering scheme, we present a measurement of three-body loss coefficients, extracted from loss curves in rubidium 85 Bose-Einstein condensates. The measurement provides new upper bounds on the three-body loss coefficients at the scattering lengths considered.