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 wavevector 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 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 ultra-cold atom setup as a tunable platform studying quantum aspects of the Pokrovsky-Talapov theory in and out-of-equilibrium.

15 pages, 8 figures

References in corpus (51)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Probing many-body dynamics on a 51-atom quantum simulator
• Quantum computation with trapped polar molecules
• Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• Relaxation and Pre-thermalization in an Isolated Quantum System
• Spinor Bose-Einstein condensates
• Matter-wave interferometry in a double well on an atom chip
• Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms
• Creation of effective magnetic fields in optical lattices: The Hofstadter butterfly for cold neutral atoms
• Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms
• Spontaneous Inter-layer Coherence in Double-Layer Quantum-Hall Systems I: Charged Vortices and Kosterlitz-Thouless Phase Transitions
• Experimental Observation of a Generalized Gibbs Ensemble
• Visualizing edge states with an atomic Bose gas in the quantum Hall regime
• Fermi gases in one dimension: From Bethe Ansatz to experiments
• Probing entanglement in a many-body-localized system
• The Unitary Fermi Gas: From Monte Carlo to Density Functionals
• Optical clock intercomparison with $6\times 10^{-19}$ precision in one hour
• Local emergence of thermal correlations in an isolated quantum many-body system
• Quantum Ferromagnetism and Phase Transitions in Double-Layer Quantum Hall Systems
• On solving quantum many-body problems by experiment
• Competing density-wave orders in a one-dimensional hard-boson model
• Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons
• Spin-exchange interactions of spin-one bosons in optical lattices: singlet, nematic and dimerized Phases
• Radio-frequency dressed state potentials for neutral atoms
• Incommensurate spin correlations in Heisenberg spin-1/2 zig-zag ladders
• Adiabatic radio frequency potentials for the coherent manipulation of matter waves
• Linear response theory for a pair of coupled one-dimensional condensates of interacting atoms
• Commensurate-incommensurate transition of cold atoms in an optical lattice
• The dynamics and prethermalization of one dimensional quantum systems probed through the full distributions of quantum noise
• Recurrences in an isolated quantum many-body system
• Tuning friction atom-by-atom in an ion-crystal simulator
• Fulde-Ferrell-Larkin-Ovchinnikov superfluidity in one-dimensional optical lattices
• Digital-Analog Quantum Simulations with Superconducting Circuits
• Spontaneous Interlayer Coherence in Double-Layer Quantum Hall Systems: Symmetry Breaking Interactions, In-Plane Fields and Phase Solitons
• Frenkel-Kontorova model with cold trapped ions
• Prethermalization Revealed by the Relaxation Dynamics of Full Distribution Functions
• Designing Arbitrary One-dimensional Potentials on an Atom Chip
• Mott Transition for Strongly-Interacting 1D Bosons in a Shallow Periodic Potential
• Dynamical structure factor of the anisotropic Heisenberg chain in a transverse field
• Relative phase fluctuations of two coupled one-dimensional condensates
• Nano-friction in cavity quantum electrodynamics
• Correlations in the Sine-Gordon Model with Finite Soliton Density
• Commensurability effects for fermionic atoms trapped in 1D optical lattices
• Scaling Exponents in the Incommensurate Phase of the Sine-Gordon and U(1) Thirring Models
• Coherence and Josephson oscillations between two tunnel-coupled one-dimensional atomic quasicondensates at finite temperature
• Plastic depinning in artificial vortex channels: competition between bulk and boundary nucleation
• Solitons: from Charge Density Waves to FFLO in superconductors
• Pokrovsky-Talapov Model at finite temperature: a renormalization-group analysis
• Strongly interacting bosons in a 1D optical lattice at incommensurate densities
• Exact Results for Thermodynamics of the Classical Field Theories: Sine- and Sinh-Gordon Models

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