superfluid-Mott Insulator Quantum Phase Transition Research Articles

Superfluid Mott-insulator quantum phase transition in an open cavity optomagnonic system

We investigated the superfluid Mott-insulator phase transition within an open coupled cavity optomagnonic array system. Based on the quasibosonic approach and employing perturbation approximation and mean-field theory, we obtain the time-dependent analytical superfluid order parameter. Our analysis revealed that dissipation induces decoherence within the system, while a strong magnon-cavity coupling enhances coherence significantly. Moreover, we explored the mechanisms by which increasing the magnon-cavity coupling strength drives the system towards the superfluid phase. The work holds significant guidance for the study of superfluidMott insulator phase transition under dissipative conditions, and providing a reliable reference for experimental implementation in open quantum systems.

Superfluid–Mott-insulator quantum phase transition in a cavity optomagnonic system

The emerging hybrid cavity optomagnonic system is a very promising quantum information processing platform for its strong or ultrastrong photon-magnon interaction on the scale of micrometers in the experiment. In this paper, the superfluid-Mott insulator quantum phase transition in a two-dimensional cavity optomagnonic array system has been studied based on this characteristic. The analytical solution of the critical hopping rate is obtained by the mean field approach, second perturbation theory and Landau second order phase transition theory. The numerical results show that the increasing coupling strength and the positive detunings of the photon and the magnon favor the coherence and then the stable areas of Mott lobes are compressed correspondingly. Moreover, the analytical results agree with the numerical ones when the total excitation number is lower. Finally, an effective repulsive potential is constructed to exhibit the corresponding mechanism. The results obtained here provide an experimentally feasible scheme for characterizing the quantum phase transitions in a cavity optomagnonic array system, which will offer valuable insight for quantum simulations.

Enhanced nonlinear quantum metrology with weakly coupled solitons in the presence of particle losses

The estimation of physical parameters with Heisenberg sensitivity and beyond is one of the crucial problems for current quantum metrology. However, unavoidable lossy effect is commonly believed to be the main obstacle when applying fragile quantum states. To utilize the lossy quantum metrology, we offer an interferometric procedure for phase parameters estimation at the Heisenberg (up to 1/N) and super-Heisenberg (up to 1/N^3) scaling levels in the framework of the linear and nonlinear metrology approaches, respectively. The heart of our setup is the novel soliton Josephson Junction (SJJ) system providing the formation of the quantum probe, i.e, the entangled Fock (N00N-like) state, beyond the superfluid-Mott insulator quantum phase transition point. We illustrate that such states are close to the optimal ones even with moderate losses. The enhancement of phase estimation accuracy remains feasible both for the linear and nonlinear metrologies with the SJJs, and allows further improvement for the current experiments performed with atomic condensate solitons with a mesoscopic number of particles.

Evidence from on-site atom number fluctuations for a quantum Berezinskii-Kosterlitz-Thouless transition in the one-dimensional Bose-Hubbard model

We study the one-dimensional Bose-Hubbard model describing the superfluid-Mott insulator quantum phase transition of cold atoms in optical lattices. We show that derivatives of the variance of the on-site atom number occupation, computed with respect to the parameter driving the transition, have extrema that are located off the critical point even in the thermodynamic limit. We discuss whether such extrema provide solid evidence of the quantum Berezinskii-Kosterlitz-Thouless transition taking place in this system. The calculations are done for systems with the mean number of atoms per lattice site equal to either one or two. They also characterize the nearest-neighbor correlation function, which is typically discussed in the context of time-of-flight images of cold atoms.

Superfluid–Mott insulator quantum phase transition in hybrid cavity optomechanical arrays

A two-dimensional hybrid cavity optomechanical array formed by an optomechanical cavity embedded with a two-level atom in each site is introduced to discuss the superfluid–Mott insulator quantum phase transition of light. On account of the optomechanical coupling effects stemmed from the coupled movable oscillator, the energy spectrum of the system changes, and an effective on-site repulsive interaction is reformed by modulating the optomechanically controlled parameters. By adjusting the detuning, an intersection between different critical chemical potentials can be found together with a disappearance of certain Mott lobes physically. The pronounced optomechanical coupling strength is in favor of the Mott insulator phase due to the enhanced effective on-site interactions. Additionally, the Kerr-nonlinearity reduces the average excitation of the high Mott insulator state and diminishes the superfluid regime. The results obtained here provide a novel image for characterizing the quantum phase transitions in optomechanical array systems, which will offer valuable insight for quantum simulations.

Superfluid–Mott-insulator quantum phase transition of light in a two-mode cavity array with ultrastrong coupling

In this paper we construct a new type of cavity array, in each cavity of which multiple two-level atoms interact with two independent photon modes. This system can be totally governed by a two-mode Dicke-lattice model, which includes all of the counter-rotating terms and therefore works well in the ultrastrong coupling regime achieved in recent experiments. Attributed to its special atom-photon coupling scheme, this model supports a global conserved excitation and a continuous $U(1)$ symmetry, rather than the discrete $Z_{2}$ symmetry in the standard Dicke-lattice model. This distinct change of symmetry via adding an extra photon mode strongly impacts the nature of photon localization/delocalization behavior. Specifically, the atom-photon interaction features stable Mott-lobe structures of photons and a second-order superfluid-Mott-insulator phase transition, which share similarities with the Jaynes-Cummings-lattice and Bose-Hubbard models. More interestingly, the Mott-lobe structures predicted here depend crucially on the atom number of each site. We also show that our model can be mapped into a continuous $XX$ spin model. Finally, we propose a scheme to implement the introduced cavity array in circuit quantum electrodynamics. This work broadens our understanding of strongly-correlated photons.

Tuning the quantum phase transition of bosons in optical lattices via periodic modulation of thes-wave scattering length

We consider interacting bosons in a 2D square and a 3D cubic optical lattice with a periodic modulation of the s-wave scattering length. At first we map the underlying periodically driven Bose-Hubbard model for large enough driving frequencies approximately to an effective time-independent Hamiltonian with a conditional hopping. Combining different analytical approaches with quantum Monte Carlo simulations then reveals that the superfluid-Mott insulator quantum phase transition still exists despite the periodic driving and that the location of the quantum phase boundary turns out to depend quite sensitively on the driving amplitude. A more detailed quantitative analysis shows even that the effect of driving can be described within the usual Bose-Hubbard model provided that the hopping is rescaled appropriately with the driving amplitude. This finding indicates that the Bose-Hubbard model with a periodically driven s-wave scattering length and the usual Bose-Hubbard model belong to the same universality class from the point of view of critical phenomena.

Magnetothermoelectric response near quantum critical points

Following on from our previous work [M. J. Bhaseen , Phys. Rev. Lett. 98, 166801 (2007)] we examine the finite temperature magnetothermoelectric response in the vicinity of a quantum critical point (QCP). We begin with general scaling considerations relevant to an arbitrary QCP, either with or without Lorentz invariance, and in arbitrary dimension. In view of the broad connections to high-temperature superconductivity and cold atomic gases, we focus on the quantum critical fluctuations of the relativistic Landau-Ginzburg theory. This paradigmatic model arises in many contexts and describes the (particle-hole symmetric) superfluid-Mott insulator quantum phase transition in the Bose-Hubbard model. The application of a magnetic field opens up a wide range of physical observables, and we present a detailed overview of the charge and thermal transport and thermodynamic response. We combine several different approaches including the epsilon expansion and associated quantum Boltzmann equation, entropy drift, and arguments based on Lorentz invariance. The results differ markedly from the zero-field case, and we include an extended discussion of the finite thermal conductivity which emerges in the presence of a magnetic field. We derive an integral equation that governs its response and explore the crossover upon changing the magnetic field. This equation may be interpreted as a projection equation in the low-field limit, and clearly highlights the important role of collision invariants (or zero modes) in the hydrodynamic regime. Using an epsilon expansion around three dimensions, our analytic and numerical results interpolate between our previously published value and the exact limit of two-dimensional relativistic magnetohydrodynamics.

SU(2)-Invariant Continuum Theory for an Unconventional Phase Transition in a Three-Dimensional Classical Dimer Model

We derive a continuum theory for the phase transition in a classical dimer model on the cubic lattice, observed in recent Monte Carlo simulations. Our derivation relies on the mapping from a three-dimensional classical problem to a two-dimensional quantum problem, by which the dimer model is related to a model of hard-core bosons on the kagome lattice. The dimer-ordering transition becomes a superfluid-Mott insulator quantum phase transition at fractional filling, described by an SU(2)-invariant continuum theory.

Phonon Superfluids in Sets of Trapped Ions

We show that transverse phonons in a set of trapped ions under the action of lasers are described by an interacting boson model whose parameters can be externally adjusted. If the radial trapping frequency is large enough, the system is described by a Bose–Hubbard model, in which hopping of the phonons between different ions is provided by the Coulomb interaction. On the other hand, the non-linear terms in the interaction of the ions with a standing-wave provide us with the phonon–phonon interaction. We investigate the possibility of observing several quantum many—body phenomena, including (quasi)Bose–Einstein Condensation as well as a superfluid-Mott insulator quantum phase transition.

Equilibrium and Dynamical Properties of the Boson Hubbard Model in One Dimension

We describe quantum monte carlo simulations of the static and dynamic properties of the one dimensional boson Hubbard model, emphasizing the extent to which an external confining potential modifies the behavior. While the superfluid-Mott insulator quantum phase transition no longer exists when the system is confined, Mott and superfluid regions persist locally in the system. We construct a ‘state diagram’ based on the local density and compressibility profiles. Solitons present in the dynamics of the unconfined system survive the addition of a trapping potential.

Bose-Einstein Condensation and Strong-Correlation Behavior of Phonons in Ion Traps

We show that the dynamics of phonons in a set of trapped ions interacting with lasers is described by a Bose-Hubbard model whose parameters can be externally adjusted. We investigate the possibility of observing several quantum many-body phenomena, including Bose-Einstein condensation as well as a superfluid-Mott insulator quantum phase transition.

Superfluid-Insulator Transition of a Bose–Einstein Condensation in a Periodic Potential and Its Interference Pattern

Recent experiments have succeeded in observing the superfluid-Mott insulator quantum phase transition of an alkali atomic Bose–Einstein condensate in an optical lattice potential. Motivated by this work, we studied the two-dimensional Bose gas in a periodic potential by analyzing the Gross–Pitaevskii equation. We found evidence of a superfluid-insulator transition that occurs as the potential depth of the lattice is increased. For the periodic potential, the phase of the macroscopic wave function in the ground state is localized in each potential minimum. Also, according to the resugts using the Hartree–Fock–Bogoliubov equation, an energy gap appears in the lowest excitation state. We then added a parabolic trapping potential to the periodic potential and studied how the dynamics of the wave function and its interference pattern depend on the initial ground state. For the initial ground state localized by the deep periodic potential, the wave function oscillates in the central potential minimum after removing only the trapping potential. After turning off both the trapping and periodic potentials, the wave packets with periodicity escape from the condensate.