Propagation of Sound in a Bose-Einstein Condensate

Andrews, M. R.; Kurn, D. M.; Miesner, H.-J.; Durfee, Dallin; Townsend, C. G.; Inouye, S.; Ketterle, Wolfgang

doi:10.1103/physrevlett.79.553

Cited by 446 publications

(502 citation statements)

References 21 publications

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“…By measuring the phase shift via interference, the state of the BEC can be inferred. The PCI measurement does not destroy the atomic condensate, it can be applied repeatedly [42,43] on the same atomic sample. This also amounts to an estimate of S z , but is not a strong measurement and instead results in some dephasing of the coherence between the levels [44].…”

Section: Experimental Implementationmentioning

confidence: 99%

Macroscopic quantum information processing using spin coherent states

Byrnes

Rosseau

Khosla

et al. 2015

Optics Communications

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Previously a new scheme of quantum information processing based on spin coherent states of two component Bose-Einstein condensates was proposed (Byrnes et al. Phys. Rev. A 85, 40306(R)). In this paper we give a more detailed exposition of the scheme, expanding on several aspects that were not discussed in full previously. The basic concept of the scheme is that spin coherent states are used instead of qubits to encode qubit information, and manipulated using collective spin operators. The scheme goes beyond the continuous variable regime such that the full space of the Bloch sphere is used. We construct a general framework for quantum algorithms to be executed using multiple spin coherent states, which are individually controlled. We illustrate the scheme by applications to quantum information protocols, and discuss possible experimental implementations. Decoherence effects are analyzed under both general conditions and for the experimental implementation proposed.

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Section: Experimental Implementationmentioning

confidence: 99%

Macroscopic quantum information processing using spin coherent states

Byrnes

Rosseau

Khosla

et al. 2015

Optics Communications

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“…Recently, a highly anisotropic, quasi one-dimensional trap has been designed [5]. Up to now, the possibility of BEC in one dimension has mainly been discussed for the noninteracting Bose gas [6,7].…”

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confidence: 99%

“…A typical value for ω ⊥ which has been realized in the experiments performed at the MIT by the Ketterle group [5] is 2π·240Hz. In order to realize a one-dimensional Bose gas for this value of ω ⊥ the temperature has to be lower than 1.8nK.…”

mentioning

confidence: 99%

“…PACS: 03.75.Fi, 05.30.jp, 32.80.Pj, 67.90.+z, 71.10.Pm The experimental realization of Bose-Einstein condensation (BEC) in atomic vapors of 87 Rb [1] and 23 Na [2,3] has attracted a lot of interest [4]. Recently, a highly anisotropic, quasi one-dimensional trap has been designed [5]. Up to now, the possibility of BEC in one dimension has mainly been discussed for the noninteracting Bose gas [6,7].…”

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confidence: 99%

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Trapped one-dimensional Bose gas as a Luttinger liquid

1998

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The low-energy fluctuations of a trapped, interacting quasi one-dimensional Bose gas are studied. Our considerations apply to experiments with highly anisotropic traps. We show that under suitable experimental conditions the system can be described as a Luttinger liquid. This implies that the correlation function of the bosons decays algebraically preventing Bose-Einstein condensation. At significantly lower temperatures a finite size gap destroys the Luttinger liquid picture and BoseEinstein condensation is again possible. PACS: 03.75.Fi, 05.30.jp, 32.80.Pj, 67.90.+z, 71.10.Pm The experimental realization of Bose-Einstein condensation (BEC) in atomic vapors of 87 Rb [1] and 23 Na [2,3] has attracted a lot of interest [4]. Recently, a highly anisotropic, quasi one-dimensional trap has been designed [5]. Up to now, the possibility of BEC in one dimension has mainly been discussed for the noninteracting Bose gas [6,7]. The role of dimensionality has been carefully examined for the ideal bose gas by van Druten and Ketterle [8]. In one dimension the interaction between bosons plays an essential role due to the strong constraint in phase space [9]. The question of BEC in a quasi one-dimensional system is therefore more complicated. The purpose of this paper is to demonstrate that under suitable experimental conditions the low energy excitations of this system are described by a Luttinger liquid (LL) [10] model. The superfluid correlations of a LL decay algebraically and the system is not Bose condensed. At much lower temperatures which are determined by the extension of the trap in the longitudinal direction the spectrum of the phase fluctuations is again cut off by finite size effects and the bosons could condense again.The realization of a Luttinger liquid in a onedimensional Bose gas would be a highly non-trivial example of an interacting quantum liquid. Fermionic systems which are believed to be described by a Luttinger liquid include quasi one-dimensional organic metals [11], magnetic chain compounds,quantum wires and edge states in the Quantum Hall Effect. While these systems are always embedded in a three-dimensional matrix and thus show a crossover to a three-dimensional behavior at low temperatures, the trapped one-dimensional Bose gas would provide a clean testing ground for the concept of a Luttinger liquid.The paper is organized as follows: First we discuss the circumstances under which a trapped Bose gas can be considered as a one-dimensional quantum system. Next we demonstrate in an explicit calculation that there is a gapless mode with a linear dispersion. We show that the Hamiltonian of the low-lying excitations can be identified as that of a Luttinger liquid and therefore the densitydensity correlation function decays algebraically. In the reminder of the paper we discuss the implication of the algebraic decay of the particle-particle correlation function for BEC and review the properties of a Luttinger liquid. We consider the Bose gas in a cylindrical symmetric trap confined to the z-axis by a ti...

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“…BECs are superfluid as they posses a finite sound speed [4,5,6] and reduced long wavelength scattering [7,8]. The other important bosonic superfluid is He 4 [5,9].…”

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On the Existence of Roton Excitations in Bose?Einstein Condensates: Signature of Proximity to a Mott Insulating Phase

Nazario

Santiago

2004

Journal of Low Temperature Physics

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Within the last decade, artificially engineered Bose Einstein Condensation has been achieved in atomic systems. Bose Einstein Condensates are superfluids just like bosonic Helium is and all interacting bosonic fluids are expected to be at low enough temperatures. One difference between the two systems is that superfluid Helium exhibits roton excitations while Bose Einstein Condensates have never been observed to have such excitations. The reason for the roton minimum in Helium is its proximity to a solid phase. The roton minimum is a consequence of enhanced density fluctuations at the reciprocal lattice vector of the stillborn solid. Bose Einstein Condensates in atomic traps are not near a solid phase and therefore do not exhibit roton minimum. We conclude that if Bose Einstein Condensates in an optical lattice are tuned near a transition to a Mott insulating phase, a roton minimum will develop at a reciprocal lattice vector of the lattice. Equivalently, a peak in the structure factor will appear at such a wavevector. The smallness of the roton gap or the largeness of the structure factor peak are experimental signatures of the proximity to the Mott transition.In the present work we focus attention in the possible existence or nonexistence of roton excitations in artificially engineered Bose Einstein Condensates (BECs) [1,2,3]. BECs are superfluid as they posses a finite sound speed [4,5,6] and reduced long wavelength scattering [7,8]. The other important bosonic superfluid is He 4 [5,9]. Since BECs and He 4 are the same universal phase of matter, they share a large commonality. For example, they are both superfluids whose elementary long wavelength excitation spectrum is phononic, their ground states spontaneously break gauge invariance [10], that is their ground states exhibit macroscopic quantum coherence, and they both posses vortex excitations [11]. This is an example of universality of stable fixed points of matter. In these cases the superfluid ground state is such a fixed point. The similarities will become ever more apparent as the low energy properties BECs are studied more carefully.On the other hand, at shorter wavelengths Helium possesses a roton minimum [5,6,12] in its excitation spectrum leading to low energy excitations occurring at a specific wavevector, which are gapped and are different than long wavelength sound. These excitations can make important contributions to the dynamics and thermodynamics of the system. In BECs no such excitation has been observed and the lack of a peak in the structure factor [7] leads to the conclusion that they do not posses roton excitations. We review some of the properties of rotons in Helium and determine under what conditions will they occur in BECs.All quantum many particle systems are described by a Hamiltonian[5]where m v · ρ v/2 is the kinetic energy operator, U [ρ] is the potential energy operator, which in general can be a functional of the density operator. The density operator in first quantized notation iswith r i being the position of the ith partic...

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Propagation of Sound in a Bose-Einstein Condensate

Cited by 446 publications

References 21 publications

Macroscopic quantum information processing using spin coherent states

Macroscopic quantum information processing using spin coherent states

Trapped one-dimensional Bose gas as a Luttinger liquid

On the Existence of Roton Excitations in Bose?Einstein Condensates: Signature of Proximity to a Mott Insulating Phase

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