Interference of an Array of Independent Bose-Einstein Condensates

Hadzibabic, Zoran; Stock, Sabine; Battelier, Baptiste; Bretin, Vincent; Dalibard, Jean

doi:10.1103/physrevlett.93.180403

Cited by 202 publications

(222 citation statements)

References 28 publications

Supporting

Mentioning

210

Contrasting

Order By: Relevance

“…Since at the time of the measurement the density of the expanding condensates is relatively low, it is assumed that the situation is for all practical purposes equivalent to the noninteracting case. Since [2], better-controlled experiments in various setups (optical lattices [6], on-chip split condensates [7], nondestructive measurements [8]) have supported this view.…”

mentioning

confidence: 79%

Phase coherence and fragmentation in weakly interacting bosonic gases

Paraoanu¹

2008

Phys. Rev. A

View full text Add to dashboard Cite

We present a theory of measurement-induced interference for weakly interacting Bose-Einstein condensed (BEC) gases. The many-body state resulting from the evolution of an initial fragmented (Fock) state can be approximated as a continuous superposition of Gross-Pitaevskii (GP) states; the measurement breaks the initial phase symmetry, producing a distribution pattern corresponding to only one of the GP solutions. We discuss also analytically solvable models, such as two-mode on-chip adiabatic recombination and soliton generation in quasi one-dimensional condensates.PACS numbers: 03.75.Kk A long-standing fundamental problem in theoretical physics is to understand how relative phases are established between superfluids that have never been in contact with each other [1]. In the case of atomic BoseEinstein condensates, the first experiment of the sort was done already a decade ago [2]; strangely though, the data could be reproduced simply by assuming a phase relation between the initial condensates and using the time-dependent GP equation [3]. It soon became acknowledged, following a number of elegant proofs for the noninteracting case [4,5], that the U(1) phase symmetry is broken by the measurement process itself. Since at the time of the measurement the density of the expanding condensates is relatively low, it is assumed that the situation is for all practical purposes equivalent to the noninteracting case. Since However, in the interacting case the situation has proven to be more complicated: on one hand, it is known that interaction within each cloud tends to delocalize the phase between two condensates, leading to squeezing and to other effects similar to the Josephson effect in superconductors [9]. But BEC interference experiments require overlap of the atomic clouds, therefore the physics at work might well be different. If atoms originating from the initially independent clouds interact, it is not even clear in what sense, at the measurement time, we can talk about condensates that have not seen each other. Since fragmented states are not robust to certain classes of perturbations, it could well happen that the interaction itself would lead to phase localization [10]. Moreover, for repulsive interactions a typically phase-coherent ground state is energetically favored [9,11]. Very recently, some authors have calculated, using standard many-body techniques [12] the average of the density operator on evolving fragmented states and found out that in the interacting case the average of the density operator could display ripples which look somewhat similar to the fringes ob- * Electronic address: paraoanu@cc.hut.fi served in atomic interference experiments. It is yet not clear if a phase-coherent condensate is formed due to interactions before the measurement starts [12]. Could it be then the case that what is detected in BEC interference experiments with interaction is in fact the density and not higher-order correlations?In this paper, we present a theoretical approach that takes into account both the eff...

show abstract

mentioning

confidence: 79%

Phase coherence and fragmentation in weakly interacting bosonic gases

Paraoanu¹

2008

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…In the present case we do not observe fringe patterns that allow us to measure the droplets' relative phase, but this is mainly due to shot-to-shot noise in the in situ position and the relative spacing of the droplets since we are not yet in the far-field regime. Future studies with fixed in situ conditions prior to the time of flight could bring insight into the phase coherence of an ensemble of droplets, even in the case of a high number of them [37]. Our measurements reported here have established the existence of a novel system forming droplets stabilized by quantum fluctuations.…”

Section: Prl 116 215301 (2016) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 70%

An Arrested Implosion

Carr

Lev

2016

Physics

View full text Add to dashboard Cite

Quantum fluctuations are the origin of genuine quantum many-body effects, and can be neglected in classical mean-field phenomena. Here, we report on the observation of stable quantum droplets containing ∼800 atoms that are expected to collapse at the mean-field level due to the essentially attractive interaction. By systematic measurements on individual droplets we demonstrate quantitatively that quantum fluctuations mechanically stabilize them against the mean-field collapse. We observe in addition the interference of several droplets indicating that this stable many-body state is phase coherent. DOI: 10.1103/PhysRevLett.116.215301 Uncertainties and fluctuations around mean values are one of the key consequences of quantum mechanics. At the many-body level, they induce corrections to mean-field theory results, altering the many-body state, from a classical factorizable to an entangled state. Owing to their versatility, ultracold atom experiments offer numerous examples of interesting many-body states [1]. Among these systems, bosonic superfluids are well studied. They are described in the weakly interacting regime by a mean-field energy density proportional to the square of the particle density n 2 , with a negative prefactor in the attractive case. Since the seminal work of Lee, Huang, and Yang [2], it is known that interactions lead to a repulsive correction ∝ n 5=2 owing to quantum fluctuations. Therefore, an equilibrium between these two contributions can in principle stabilize an attractive Bose gas [3]. A similar stabilization mechanism using quantum fluctuations was proposed for an attractive Bose-Bose mixture in Ref. [4], which leads to the formation of droplets. In this reference liquidlike droplets are defined as the result of a competition between an attractive n 2 and a repulsive n 2þα term in the energy functional. Besides liquid helium droplets [5], such functionals are also used to describe atomic nuclei [6]. Here, we study a strongly dipolar Bose gas where the attractive mean-field interaction is due to the dipole-dipole interaction (DDI). This system is known to be unstable in the mean-field approximation [7]. We however show here that beyond mean-field effects lead to the stabilization of droplets. Our investigations are aimed at probing strongly dipolar Bose gases of 164 Dy, which are characterized by a dipolar length a dd ¼ μ 0 μ 2 m=12πℏ 2 ≃ 131a 0 , where a 0 is the Bohr radius with μ ¼ 9.93μ B Dy's magnetic dipole moment in units of the Bohr magneton μ B , ℏ the reduced Planck constant, and m the atomic mass. The additional short-range interaction of 164 Dy, characterized by the scattering length a has been the focus of several papers [8][9][10][11], and the background scattering length was measured to be a bg ¼ 92ð8Þa 0 , modulated by many Feshbach resonances. Thus, away from Feshbach resonances at the mean-field level the dipolar interaction dominates with ε dd;bg ¼ a dd =a bg ≃ 1.45. In a previous work [12], we have reported the observation of an instability of a dipolar Bose-Einste...

show abstract

“…In the following, the calculated results will be considered for the experimental trap parameters of Hadzibabic [13]. In Fig.1, the dependence of the condensate fraction on and α for optical potential depth and interaction parameter is illustrated.…”

Section: Thermodynamic Parametersmentioning

confidence: 99%

“…These include: the BEC transition temperature [15,16]; the heat capacity, which enabled us to discuss the order of phase transition [17,18] and the entropy of the system [19], required to investigate the adiabatic cooling of the boson system in lattice. Our results are given for the trap parameters of the Hadzibabic's et al experiment [13]: the radial and axial frequencies of the harmonic trap are I N THIS work, we investigated the thermodynamic behavior of a rotating Bose-Einstein condensation with non-zero interatomic interactions in one-dimensional optical lattice theoretically. Our system is formed by loading three dimensional boson-clouds into 1D optical lattice and subjected to rotate with angular velocity ɷ about the z axis.…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by the recent advances achieved in the experimental manipulation of rotating condensates [11,12] and of condensates loaded into optical lattices [13], we use the self-consistent HF to study the temperature dependence of the thermodynamic parameters for the rotating interacting BEC in 1D optical lattice. The effects of the rotation rate and optical potential depth are considered simultaneously.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation