Simulating a quantum commensurate-incommensurate phase transition using two Raman-coupled one-dimensional condensates

Abstract

We study a transition between a homogeneous and an inhomogeneous phase in a system of one-dimensional, Raman tunnel-coupled Bose gases. The homogeneous phase shows a flat density and phase profile, whereas the inhomogeneous ground state is characterized by periodic density ripples and a soliton staircase in the phase difference. We show that under experimentally viable conditions the transition can be tuned by the wave-vector difference Q of the Raman beams and can be described by the Pokrovsky-Talapov model for the relative phase between the two condensates. Local imaging available in atom chip experiments allows us to observe the soliton lattice directly, while modulation spectroscopy can be used to explore collective modes, such as the phonon mode arising from breaking of translation symmetry by the soliton lattice. In addition, we investigate regimes where the cold atom experiment deviates from the Pokrovsky-Talapov field theory. We predict unusual mesoscopic effects arising from the finite size of the system, such as quantized injection of solitons upon increasing Q, or the system size. For moderate values of Q above criticality, we find that the density modulations in the two gases interplay with the relative phase profile and introduce novel features in the spatial structure of the mode wave functions. Using an inhomogeneous Bogoliubov theory, we show that spatial quantum fluctuations are intertwined with the emerging soliton staircase. Finally, we comment on the prospects of the ultracold atom setup.

Many-body parametric resonances in the driven sine-Gordon model

“…These systems provide an ideal platform to prepare interesting interacting many-body states in a controlled way, and allow for probing their dynamics. One of the paradigmatic many-body models investigated in these settings is the sine-Gordon model [4], realized by coupling two parallel quasi-one-dimensional bosonic condensates in a double-well potential [5][6][7][8][9][10][11][12][13]. The experimental realization of this model enabled the demonstration and characterization of non-Gaussian higher-order correlations in the system, revealed the presence of topological soliton excitations through the full distribution of the spatially resolved relative phase between the two condensates [6], and also led to the observation of prethermalization in the nonequilibrium dynamics of the model [6,7].…”

Inhomogeneous quantum quenches in the sine-Gordon theory

“…Overall the recent experimental and theoretical progress of Ref. [101,102] and [61] lays the groundwork for the implementation of states with localised soliton density bumps similar to those considered here and the study of their dynamics under the sine-Gordon model.…”

“…On the other hand, it has been recently shown theoretically that solitons can be injected in the system using Raman coupling between the two condensates [102]. In this case the lowenergy effective description of the system follows the Pokrovsky-Talapov model [68] which corresponds to a sine-Gordon model with an additional term controlling the soliton number.…”

Many-body parametric resonances in the driven sine-Gordon model

“…These systems provide an ideal platform to prepare interesting interacting manybody states in a controlled way, and allow for probing their dynamics. One of the paradigmatic manybody models investigated in these settings is the sine-Gordon model [4], realized by coupling two parallel quasione-dimensional bosonic condensates in a double well potential [5][6][7][8][9][10][11][12]. The experimental realization of this model enabled the demonstration and characterization of non-Gaussian higher order correlations in the system, revealed the presence of topological soliton excitations through the full distribution of the spatially resolved relative phase between the two condensates [6], and also lead to the observation of prethermalization in the nonequilibrium dynamics of the model [6,7].…”