Two-Point Phase Correlations of a One-Dimensional Bosonic Josephson Junction

Abstract

We realize a one-dimensional Josephson junction using quantum degenerate Bose gases in a tunable double well potential on an atom chip. Matter wave interferometry gives direct access to the relative phase field, which reflects the interplay of thermally driven fluctuations and phase locking due to tunneling. The thermal equilibrium state is characterized by probing the full statistical distribution function of the two-point phase correlation. Comparison to a stochastic model allows to measure the coupling strength and temperature and hence a full characterization of the system.Josephson dynamics between weakly coupled macroscopic wave functions have been observed in superconductors [1,2], superfluid Helium [3,4], and recently using Bose-Einstein condensates in double well potentials [5][6][7]. The bosonic Josephson junction (BJJ) is especially interesting, as particle interactions lead to additional dynamical modes such as quantum self trapping or π phase modes [5,8] and finite temperature leads to enhanced fluctuations of the observables [9]. In contrast to other implementations, the BJJ enables complete experimental control over all relevant system parameters such as the coupling strength or relative population together with direct access to the conjugate observables number and phase. Theoretical work has mostly employed a twomode approach to describe the finite temperature equilibrium system and dynamical properties [8,10].One-dimensional (1D) Josephson junctions show a significantly enriched physical behavior, as the two involved wave functions can not be described by single quantum modes any more. The non-interacting 1D junction represents an implementation of the Sine-Gordon Hamiltonian which occurs in widespread areas of physics [11,12]. In the 1D bosonic junction interactions and finite temperature are expected to cause dynamical instabilities of the classical Josephson modes [13]. Whether quasi-static phenomena such as quantum self-trapping persist in 1D is issue of ongoing discussion [14].In this work we realize and fully characterize a onedimensional bosonic Josephson junction using quantum degenerate Bose gases in a tunable double well potential. The finite temperature equilibrium state is marked by the competing effects of thermally driven phase fluctuations and phase locking due to tunnel coupling. Fluctuations of the relative population are < 1 % and can be neglected [9]. We probe the coherence properties of the coupled system by performing matter wave interferometry. Comparing the statistical distribution function of twopoint phase correlations to a stochastic model [10,15], we measure the coupling energy or the temperature of [16,17]. We characterize two-point phase correlations of the system by measuring the statistical properties of the difference of relative phases ∆ϕ(z) = ϕ(z) − ϕ(z ).the system.The experiments are performed in a horizontally orientated double well potential, generated on an atom chip using radio-frequency (RF) induced adiabatic states [18,19]. Different double well paramet...

Experimental characterization of a quantum many-body system via higher-order correlations

“…1) [21]. Matter-wave interferometry [22][23][24] gives direct access to the spatially resolved relative phase ϕ(z) between the superfluids (see Methods).…”

“…The strength of this 'phase locking' is characterised by cos(ϕ) , a quantity that is zero for completely random phases (no phase locking) and approaches unity in the limit of strong phase locking. The value of cos(ϕ) depends on the tunnelcoupling strength as well as on the temperature [21].…”

Multimode Dynamics and Emergence of a Characteristic Length Scale in a One-Dimensional Quantum System

“…In the case of two uncoupled quasicondensates in thermal equilibrium with temperature T, the thermal phase-correlation length is given by ¼ @ 2 =mk B T [30,31]. Due to our rapid splitting process, the energy initially stored in the system is equally distributed between the different k modes of the system [12,14], resulting in thermal-like correlations characterized by an effective temperature k B T eff ¼ hĤij t¼0 ¼ g=2.…”

Two-component Bose gases with one-body and two-body couplings

“…Such systems offer a new tool to study quantum coherence in various contexts [9,25,27,30]. For instance, measurement of the relative-phase correlation function of a coupled binary Bose gas in one dimension was reported in Ref.…”

“…Early studies focused on the possibility of observing Bose-Einstein condensation [11], as well as stability conditions [1,12,13], phase separation [8,[14][15][16][17][18][19][20], and spontaneous symmetry breaking mechanisms [21][22][23][24] in twocomponent Bose-Einstein condensates. Two-component Bose gases have also been used to study phase coherence [25], Josephson like physics [26][27][28][29][30], the dynamics of spin textures [31][32][33][34], random-field-induced order effects [35,36], and twin quantum states for quantum information processing [37][38][39].…”