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arXiv:1110.4734 · Frontiers of Physics

Nonlinear quantum interferometry with Bose condensed atoms

Chaohong Lee, Jiahao Huang, Haiming Deng, Hui Dai, Jun Xu

Published Jan 21, 2012• 90 citations
arXivHTMLPDF

Abstract

In quantum interferometry, it is vital to control and utilize nonlinear interactions for the achievement of high-precision measurements. Due to their long coherence time and high controllability, ultracold atoms including Bose condensed atoms have been widely used for quantum interferometry. Here, we review recent progress in theoretical studies of quantum interferometry with Bose condensed atoms. In particular, we focus on nonlinear phenomena induced by atom-atom interactions, and how to control and utilize these nonlinear phenomena. With a mean-field description, due to atom-atom interactions, matter-wave solitons appear in the interference patterns, and macroscopic quantum self-trapping exists in Bose-Josephson junctions. With a many-body description, atom-atom interactions can generate non-classical entanglement, which can be utilized to achieve high-precision measurements beyond the standard quantum limit.

DOI
10.1007/s11467-011-0228-6

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In quantum interferometry, it is vital to control and utilize nonlinear interactions for the achievement of high-precision measurements. Due to their long coherence time and high controllability, ultracold atoms including Bose condensed atoms have been widely used for quantum interferometry. Here, we review recent progress in theoretical studies of quantum interferometry with Bose condensed atoms. In particular, we focus on nonlinear phenomena induced by atom-atom interactions, and how to control and utilize these nonlinear phenomena. With a mean-field description, due to atom-atom interactions, matter-wave solitons appear in the interference patterns, and macroscopic quantum self-trapping exists in Bose-Josephson junctions. With a many-body description, atom-atom interactions can generate non-classical entanglement, which can be utilized to achieve high-precision measurements beyond the standard quantum limit.
Interferometry with ultracold atoms promises the possibility of ultraprecise and ultrasensitive measurements in many fields of physics, and is the basis of our most precise atomic clocks. Key to a high sensitivity is the possibility to achieve long measurement times and precise readout. Ultracold atoms can be precisely manipulated at the quantum level and can be held for very long times in traps; they would therefore be an ideal setting for interferometry. In this paper, we discuss how the nonlinearities from atom–atom interactions, on the one hand, allow us to efficiently produce squeezed states for enhanced readout and, on the other hand, result in phase diffusion that limits the phase accumulation time. We find that low-dimensional geometries are favorable, with two-dimensional (2D) settings giving the smallest contribution of phase diffusion caused by atom–atom interactions. Even for time sequences generated by optimal control, the achievable minimal detectable interaction energy Δ E min is of the order of 10 −4 μ, where μ is the chemical potential of the Bose–Einstein condensate (BEC) in the trap. From these we have to conclude that for more precise measurements with atom interferometers, more sophisticated strategies, or turning off the interaction-induced dephasing during the phase accumulation stage, will be necessary.
Interferometry with ultracold atoms promises the possibility of ultraprecise and ultrasensitive measurements in many elds of physics, and is the basis of our most precise atomic clocks. Key to a high sensitivity is the possibility to achieve long measurement times and precise readout. Ultra cold atoms can be precisely manipulated at the quantum level, held for very long times in traps, and would therefore be an ideal setting for interferometry. In this paper we discuss how the non-linearities from atom-atom interactions on one hand allow to efficiently produce squeezed states for enhanced readout, but on the other hand result in phase diffusion which limits the phase accumulation time. We find that low dimensional geometries are favorable, with two-dimensional (2D) settings giving the smallest contribution of phase diffusion caused by atom-atom interactions. Even for time sequences generated by optimal control the achievable minimal detectable interaction energy ∆Emin is on the order of 10−4µ, where µ is the chemical potential of the BEC in the trap. From there we have to conclude that for more precise measurements with atom interferometers more sophisticated strategies, or turning off the interaction induced dephasing during the phase accumulation stage, will be necessary. PACS numbers: 37.25.+k,03.75.-b,37.10.Gh,02.60.Pn
This review discusses progress in the new field of coherent matter waves, in particular with respect to Bose-Einstein condensates. We give a short introduction to Bose-Einstein condensation and the theoretical description of the condensate wavefunction. We concentrate on the coherence properties of this new type of matter wave as a basis for fundamental physics and applications. The main part of this review treats various measurements and concepts in the physics with coherent matter waves. In particular we present phase manipulation methods, atom lasers, nonlinear atom optics, optical elements, interferometry and physics in optical lattices. We give an overview of the state of the art in the respective fields and discuss achievements and challenges for the future.
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.
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Abstract The review presents the methods of generation of nonlinear coherent excitations in strongly nonequilibrium Bose-condensed systems of trapped atoms and their properties. Non-ground-state Bose–Einstein condensates are represented by nonlinear coherent modes. The principal difference of nonlinear coherent modes from linear collective excitations is emphasized. Methods of generating nonlinear modes and the properties of the latter are described. Matter-wave interferometry with coherent modes is discussed, including such effects as interference patterns, internal Josephson current, Rabi oscillations, Ramsey fringes, harmonic generation, and parametric conversion. Dynamic transition between mode-locked and mode-unlocked regimes is shown to be analogous to a phase transition. Atomic squeezing and entanglement in a lattice of condensed atomic clouds with coherent modes are considered. Nonequilibrium states of trapped Bose-condensed systems, starting from weakly nonequilibrium state, vortex state, vortex turbulence, droplet or grain turbulence, and wave turbulence, are classified by means of effective Fresnel and Mach numbers. The inverse Kibble–Zurek scenario is described. A method for the formation of directed beams from atom lasers is reported.