We investigate the ground-state properties of weakly repulsive one-dimensional bosons in the presence of an attractive zero-range impurity potential. First, we derive mean-field solutions to the problem on a finite ring for the two asymptotic cases: (i) all bosons are bound to the impurity and (ii) all bosons are in a scattering state. Moreover, we derive the critical line that separates these regimes in the parameter space. In the thermodynamic limit, this critical line determines the maximum number of bosons that can be bound by the impurity potential, forming an artificial atom. Second, we validate the mean-field results using the flow equation approach and the multi-layer multi-configuration time-dependent Hartree method for atomic mixtures. While beyond-mean-field effects destroy long-range order in the Bose gas, the critical boson number is unaffected. Our findings are important for understanding such artificial atoms in low-density Bose gases with static and mobile impurities.
We identify regular structures in the globally chaotic spectra of an interacting bosonic quantum gas in tilted periodic potentials. The associated eigenstates exhibit strong localization properties on the lattice, and are dynamically robust against external perturbations.
In this article we proposed a scheme to generating steady topologically non-trivial artificial spin texture in cold atom systems. An example of generating a texture of charge one skyrmion with Laguerre-Gaussian beam was given. It provides a scheme for studying skyrmion excitations of quantum Hall ferromagnetism in cold atom systems.
We study cold atomic gases with a contact interaction and confined into one-dimension. Crossing the confinement induced resonance the correlation between the bosons increases, and introduces an effective range for the interaction potential. Using the mapping onto the sine-Gordon model and a Hubbard model in the strongly interacting regime allows us to derive the phase diagram in the presence of an optical lattice. We demonstrate the appearance of a phase transition from a Luttinger liquid with algebraic correlations into a crystalline phase with a particle on every second lattice site.
We propose to generate an artificial non-Abelian $U(3)$ gauge field by using a 2-tripod scheme, namely two tripod configurations sharing a common ground state level and driven by resonant 1-photon transitions. Using an appropriate combination of four Laguerre-Gauss and two Hermite-Gauss laser beams, we are able to produce a $U(3)$-monopole and a $U(3)$ spin-orbit coupling for both alkali and alkaline-earth atoms. This 2-tripod scheme could open the way to the study of interacting spinor condensates subjected to $U(3)$-monopoles.
For over twenty years, ultra-cold atomic systems have formed an almost perfect arena for simulating different quantum many-body phenomena and exposing their non-obvious and very often counterintuitive features. Thanks to extremely precise controllability of different parameters they are able to capture different quantum properties which were previously recognized only as theoretical curiosities. Here, we go over the current experimental progress in exploring the curious one-dimensional quantum world of fermions from the perspective of three subjectively selected trends being currently under vi…
This paper proposes a simple setup for introducing an artificial magnetic field for neutral atoms in 2D optical lattices. This setup is based on the phenomenon of photon-assisted tunneling and involves a low-frequency periodic driving of the optical lattice. This low-frequency driving does not affect the electronic structure of the atom and can be easily realized by the same means which employed to create the lattice. We also address the problem of detecting this effective magnetic field. In particular, we study the center of mass wave-packet dynamics, which is shown to exhibit certain feature…
We investigate the number fluctuations of spatially split many-boson systems employing a theorem about the maximally and minimally attainable variances of an observable. The number fluctuations of many-boson systems are given for different numbers of lattice sites and both mean-field and many-body wave functions. It is shown which states maximize the particle number fluctuations, both in lattices and double-wells. The fragmentation of the states is discussed, and it is shown that the number fluctuations of some fragmented states are identical to those of fully condensed states.
We propose that an artificial electromagnetic field can be engineered in the context of cold fermionic atoms that are coupled to a cavity mode via two-photon processes in a two-dimensional optical lattice. There is a standing-wave pump laser inducing the electric effect in one spatial direction, and a second running-wave laser beam generates the magnetic flux perpendicular to the lattice plane. In the static scenario, the bulk spectrum resembles the fractal structure of the Hofstadter butterfly and the edge mode spectrum indicates the occurrence of the quantum Hall phase. The Keldysh formulism…
A Bose-Hubbard Hamiltonian, modeling cold bosons in an optical lattice, is used to simulate the dynamics of interacting open quantum systems as subsystems a larger closed system, avoiding complications like the introduction of baths, complex absorbing potentials or absorbing boundaries. The numerically exact unitary dynamics is compared with effective descriptions of the subsystems based on non-Hermitian Hamiltonians or Lindblad master equations. The validity of popular models with constant decay rates is explicitly analyzed for decaying single and double wells. In addition we present a discre…
We investigate the single-atom transport in a two-leg ladder with only two rungs, which together with the legs, enclose an artificial magnetic flux. Here, the atoms on the two legs possess opposite onsite energies that produce an energy offeset. We find that the atom incoming from the left leg can experience from blockade to tranparency via modifying the onsite energy, hopping strength, or magnetic flux, which can be potentially used for a quantum switcher. Furthermore, the atom incoming from the left leg can also be perfectly routed into the right leg, when, intriguingly, the outgoing atom in…
We analyze the single particle quantum mechanics of an atom whose dispersion is modified by spin orbit coupling to Raman lasers. We calculate how the novel dispersion leads to unusual single particle physics. We focus on the symmetry of the ground state wavefunction in different potentials.
The BEC regime of a cold fermi gas is characterised by coupled atoms (dimers) which, superficially, look like elementary bosons. We examine how simply-bosonic they really are; firstly, in the Bogoliubov approximation and further, through new actions for the BEC regime in which dimers are represented by coupled Gross-Pitaevskii fields. We find identity at the level of the Bogoliubov approximation in the deep BEC regime, permitting a simple Gross-Pitaevskii description. This fails rapidly as we move towards the BCS regime. However, even in the deep BEC regime there is an intrinsic difference if …
The entropy of the coexisting gas of ultra cold fermionic atoms and Bosonic molecular condensate confined in a magnetic trap has been calculated from equation of motion approaches. We have found that the entropy production depends not only to the Feshbach resonance and but also under certain limits to Rabi type oscillation and Bose Josephson junction type oscillation.
This dissertation presents theoretical investigations of universality and finite-range corrections in few- and many-boson systems. The main focus is on ultra-cold atomic gases seen both from the three-body, many-body, and mean-field perspective. Topics include corrections to Efimov physics, the N-body Efimov effect, two-body correlations in condensates and higher-order interactions in mean-field BECs.
Recent progress in cooling and trapping of polarized clouds of chromium $^{52}Cr$, dysprosium $^{164}Dy$ and erbium $^{168}Er$ opens a road-map to quantum systems where shapes of inter-particle interactions can be customized. The main purpose of this work is to get a deeper insight on a role which the overall shape of the inter-particle interaction plays in a context of trapped ultra-cold bosons. We show that strong inter-particle repulsion inevitably leads to multi-hump fragmentation of the ground state. The fragmentation phenomenon is universal -- it takes place in traps of different dimensi…
Ultra-cold bosons in zig-zag optical lattices present a rich physics due to the interplay between frustration, induced by lattice geometry, two-body interaction and three-body constraint. Unconstrained bosons may develop chiral superfluidity and a Mott-insulator even at vanishingly small interactions. Bosons with a three-body constraint allow for a Haldane-insulator phase in non-polar gases, as well as pair-superfluidity and density wave phases for attractive interactions. These phases may be created and detected within the current state of the art techniques.
We consider one dimensional potential trap that connects two reservoirs containing cold Bose atoms. The thermal current and single-particle bosonic Green functions are calculated under non-equilibrium conditions. The bosonic statistics leads to Luttinger liquid state with non-linear spectrum of collective modes. This results in suppression of thermal current at low temperatures and affects the single-particle Green functions.
We study the thermalization of excitations generated by spontaneous emission events for cold bosons in an optical lattice. Computing the dynamics described by the many-body master equation, we characterize equilibration timescales in different parameter regimes. For simple observables, we find regimes in which the system relaxes rapidly to values in agreement with a thermal distribution, and others where thermalization does not occur on typical experimental timescales. Because spontaneous emissions lead effectively to a local quantum quench, this behavior is strongly dependent on the low-energ…
We argue that the Fermi-Hubbard Hamiltonian describing the physics of ultracold atoms on optical lattices in the presence of artificial non-Abelian gauge fields, is exactly equivalent to the gauge theory Hamiltonian describing Dirac fermions in the lattice. We show that it is possible to couple the Dirac fermions to an "artificial" gravitational field, i.e. to consider the Dirac physics in a curved spacetime. We identify the special class of spacetime metrics that admit a simple realization in terms of a Fermi-Hubbard model subjected to an artificial SU(2) field, corresponding to position depe…
We study theoretically quantum dynamics of interacting bosons in artificial magnetic fields as engineered in recent ultracold atomic experiments, where quantum cyclotron orbital motion has been observed. With exact numerical simulations and perturbative analyses, we find that interactions induce damping in the cyclotron motion. The damping time is found to be dependent on interaction and tunneling strengths monotonically, while its dependence on magnetic flux is non-monotonic. Sufficiently strong interactions would render bosons dynamically localized inhibiting the cyclotron motion. The dampin…
We develop and apply the multi-layer multi-configuration time-dependent Hartree method for bosons, which represents an ab initio method for investigating the non-equilibrium quantum dynamics of multi-species bosonic systems. Its multi-layer feature allows for tailoring the wave function ansatz in order to describe intra- and inter-species correlations accurately and efficiently. To demonstrate the beneficial scaling and the efficiency of the method, we explore the correlated tunneling dynamics of two species with repulsive intra- and inter-species interactions, to which a third species with va…
Artificial gauge fields are a unique way of manipulating the motional state of cold atoms. Here we propose the use of artificial gauge fields -- obtained e.g. via lattice shaking -- to perform primary noise thermometry of cold atoms in optical lattices - not requiring any form of prior calibration. The proposed thermometric scheme relies on fundamental fluctuation-dissipation relations, connecting the global response to the variation of the applied gauge field and the fluctuation of quantities related to the momentum distribution (such as the average kinetic energy or the average current). We …
We analyze a scheme for preparation of magnetically ordered states of two-component bosonic atoms in optical lattices. We compute the dynamics during adiabatic and optimized time-dependent ramps to produce ground states of effective spin Hamiltonians, and determine the robustness to decoherence for realistic experimental system sizes and timescales. Ramping parameters near a phase transition point in both effective spin-1/2 and spin-1 models produces entangled spin-symmetric states that have potential future applications in quantum enhanced measurement. The preparation of these states and thei…
Using the micro-canonical picture of transport -- a framework ideally suited to describe the dynamics of closed quantum systems such as ultra-cold atom experiments -- we show that the exact dynamics of non-interacting fermions and bosons exhibit very different transport properties when the system is set out of equilibrium by removing the particles from half of the lattice. We find that fermions rapidly develop a finite quasi steady-state current reminiscent of electronic transport in nanoscale systems. This result is robust -- it occurs with or without a harmonic confining potential and at zer…
Ultracold bosons in a triangular lattice are a promising candidate for observing quantum spin liquid behavior. Here we investigate, for such system, the role of a harmonic trap giving rise to an inhomogeneous density. We construct a modified spin-wave theory for arbitrary filling, and predict the breakdown of order for certain values of the lattice anisotropy. These regimes, identified with the spin liquid phases, are found to be quite robust upon changes in the filling factor. This result is backed by an exact diagonalization study on a small lattice.
We present a construction of an improved two-mode model for modeling the dynamics of interacting ultra-cold bosons confined in a one-dimensional double well trap. Unlike in the typically used two-mode model based on the lowest single-particle eigenstates of the external potential, the improved model uses a basis of properly chosen effective wave functions originating in the many-body model. Accuracy of the improved model is examined and it is shown that within a certain limit of inter-particle interaction strength, the model recovers an exact evolution of the wells' populations much more close…
We consider the dynamics of two-dimensional interacting ultracold bosons triggered by suddenly switching on an artificial gauge field. The system is initialized in the ground state of a harmonic trapping potential. As a function of the strength of the applied artificial gauge, we analyze the emergent dynamics by monitoring the angular momentum, the fragmentation as well the entropy and variance of the entropy of absorption or single-shot images. We solve the underlying time-dependent many-boson Schrödinger equation using the multiconfigurational time-dependent Hartree method for indistinguisha…
The extended effective multiorbital Bose-Hubbard-type Hamiltonian which takes into account higher Bloch bands, is discussed for boson systems in optical lattices, with emphasis on dynamical properties, in relation with current experiments. It is shown that the renormalization of Hamiltonian parameters depends on the dimension of the problem studied. Therefore, mean field phase diagrams do not scale with the coordination number of the lattice. The effect of Hamiltonian parameters renormalization on the dynamics in reduced one-dimensional optical lattice potential is analyzed. We study both the …
The possibility of realizing bosonic fractional quantum Hall effect in ultra-cold atomic systems suggests a new route to producing and manipulating anyons, by introducing auxiliary bosons of a different species that capture quasiholes and thus inherit their non-trivial braiding properties. States with localized quasiholes at any desired locations can be obtained by annihilating the auxiliary bosons at those locations. We explore how this method can be used to generate non-Abelian quasiholes of the Moore-Read Pfaffian state for bosons at filling factor $ν=1$. We show that a Hamiltonian with an …
Cold atoms in an optical lattice with brick-wall geometry have been used to mimic graphene, a two-dimensional material with characteristic Dirac excitations. Here we propose to bring such artificial graphene into the proximity of a second atomic layer with a square lattice geometry. For non-interacting fermions, we find that such bilayer system undergoes a phase transition from a graphene-like semi-metal phase, characterized by a band structure with Dirac points, to a gapped band insulator phase. In the presence of attractive interactions between fermions with pseudospin-1/2 degree of freedom,…
A study of an interacting system of bosons in a ring trap at a finite temperature is presented. We consider a gas with contact and long-range dipolar interactions within a framework of the classical fields approximation. For a repulsive gas we have obtained coherence length, population of the ground state and its fluctuations as a function of temperature. In the case of an attractive gas we study local density fluctuations. Additionally, we exactly calculate the partition function for the ideal gas in the canonical ensemble and derive several other macroscopic state functions.
Ultracold atoms in optical lattices undergo a quantum phase transition from a superfluid to a Mott insulator as the lattice potential depth is increased. We describe an approximate theory of interacting bosons in optical lattices which provides a qualitative description of both superfluid and insulator states. The theory is based on a change of variables in which the boson coherent state amplitude is replaced by an effective potential which promotes phase coherence between different number states on each lattice site. It is illustrated here by applying it to uniform and fully frustrated lattic…
We study dynamics of two interacting ultra cold Bose atoms in a harmonic oscillator potential in one spatial dimension. Making use of the exact solution of the eigenvalue problem of a particle in the delta-like potential we study time evolution of initially separable state of two particles. The corresponding time dependent single particle density matrix is obtained and diagonalized and single particle orbitals are found. This allows to study decoherence as well as creation of entanglement during the dynamics. The evolution of the orbital corresponding to the largest eigenvalue is then compared…
This article is a report of Projet bibliographique of M1 at École Normale Supérieure. In this article we reviewed the historical developments in artificial gauge fields and spin-orbit couplings in cold atom systems. We resorted to origins of literatures to trace the ideas of the developments. For pedagogical purposes, we tried to work out examples carefully and clearly, to verified the validity of various approximations and arguments in detail, and to give clear physical and mathematical pictures of the problems that we discussed. The first part of this article introduced the fundamental conce…
We develop a theory for interacting fermions in the presence of spin-orbit coupling and Zeeman fields, and show that many new superfluids phases, which are topological in nature, emerge. Depending on values of spin-orbit coupling, Zeeman fields, and interactions, initially gapped s-wave superfluids acquire p-wave, d-wave, f-wave and higher angular momentum components, which produce zeros in the excitation spectrum, rendering the superfluid gapless. Several multi-critical points, which separate topological superfluid phases from normal or non-uniform, are accessible depending on spin-orbit coup…
We discuss the Chern number spectrum of ultra-cold fermions in square optical lattices as a function of artificial magnetic, Zeeman and spin-orbit fields that can be tuned independently. We show the existence of topological quantum phase transitions induced by Zeeman and spin-orbit fields, where the total number and chirality of edge states change for fixed magnetic flux ratio, thus leading to topological-insulator phases which are different from those found at zero Zeeman and spin-orbit fields. We construct phase diagrams of chemical potential versus Zeeman field or spin-orbit coupling and ch…
This is a review of recent developments in Monte Carlo methods in the field of ultra cold gases. For bosonic atoms in an optical lattice we discuss path integral Monte Carlo simulations with worm updates and show the excellent agreement with cold atom experiments. We also review recent progress in simulating bosonic systems with long-range interactions, disordered bosons, mixtures of bosons, and spinful bosonic systems. For repulsive fermionic systems determinantal methods at half filling are sign free, but in general no sign-free method exists. We review the developments in diagrammatic Monte…
We show that the recently developed optical lattices with Peierls substitution -- which can be modeled as a lattice with a complex tunneling coefficient -- may be used to induce controllable quantum transport of ultra-cold atoms. In particular, we show that by ramping up the phase of the complex tunneling coefficient in a spatially uniform fashion, a finite quasi steady-state current (QSSC) ensues from the exact dynamics of non-interacting fermions. The direction and magnitude of the current can be controlled by the overall phase difference but not the details of the ramp. The entanglement ent…
We calculate the time-of-flight patterns of strongly interacting bosons confined in two-dimensional square lattice in the presence of an artificial magnetic field using quantum rotor model that is inherently combined with the Bogolyubov approach. We consider various geometries of the magnetic flux, which are expected to be realizable, or have already been implemented in experimental settings. The flexibility of the method let us to study cases of the artificial magnetic field being uniform, staggered or forming a checkerboard configuration. Effects of additional temporal modulation of the opti…
We study the $\mathbb{Z}_2$ Bose-Hubbard model at incommensurate densities, which describes a one-dimensional system of interacting bosons whose tunneling is dressed by a dynamical $\mathbb{Z}_2$ field. At commensurate densities, the model is known to host intertwined topological phases, where long-range order coexists with non-trivial topological properties. This interplay between spontaneous symmetry breaking (SSB) and topological symmetry protection gives rise to interesting fractional topological phenomena when the system is doped to certain incommensurate fillings. In particular, we hereb…
We discuss topological phase transitions in ultra-cold Fermi superfluids induced by interactions and artificial spin orbit fields. We construct the phase diagram for population imbalanced systems at zero and finite temperatures, and analyze spectroscopic and thermodynamic properties to characterize various phase transitions. For balanced systems, the evolution from BCS to BEC superfluids in the presence of spin-orbit effects is only a crossover as the system remains fully gapped, even though a triplet component of the order parameter emerges. However, for imbalanced populations, spin-orbit fie…
We discuss a class of quantum theories which exhibit a sharply increased memory storage capacity due to emergent gapless degrees of freedom. Their realization, both theoretical and experimental, is of great interest. On the one hand, such systems are motivated from a quantum information point of view. On the other hand, they can provide a framework for simulating systems with enhanced capacity of pattern storage, such as black holes and neural networks. In this paper, we develop an analytic method that enables us to find critical states with increased storage capabilities in a generic system o…
We investigate the strongly correlated effect of cold atoms in triangular optical lattice by dynamical cluster approximation combining with the continuous time quantum Monte Carlo method proposed recently. It is found the double occupancy is suppressed as the atomic interaction increases. By calculating the density of states, we show how the system evolves from Fermi liquid with an obvious quasi-particle peak into Mott insulator with an opened gap for increasing interaction. The transition between Fermi liquid and pseudogap shows a reentrant behavior due to the Kondo effect. At low temperature…
Many-body densities and correlation functions are of paramount importance for understanding quantum many-body physics. Here, we present a method to compute them; our approach is general and based on the action of bosonic or fermionic annihilation field operators on the many-body wavefunction. We analyze $N = 6$ quasi-one-dimensional harmonically-trapped bosons with weak to strong contact interaction strength up to the Tonks-Girardeau limit with infinite repulsion using the MultiConfigurational Time-Dependent Hartree method for indistinguishable particles (MCTDH-X). We compare our MCTDH-X solut…
A density-dependent gauge field may induce density-induced geometric frustration, leading to a non-trivial interplay between density modulation and frustration, which we illustrate for the particular case of ultra-cold bosons in zig-zag optical lattices with a density-dependent hopping. We show that the density-induced frustration leads in a rich landscape of quantum phases, including Mott and bond-order insulators, two-component superfluids, chiral superfluids, and partially-paired superfluids. We show as well that the density-dependent hopping results in an effective repulsive or attractive …
We investigate the quantum anomalous Hall effect in a mixture of ultra-cold neutral bosons and fermions held on a hexagonal optical lattice. In the strong atom-atom interaction limit, composite fermions composed of one fermion with bosons or bosonic holes in the mixture are formed. Such composite fermions have already been generated successfully in experiment [Nat. Phys. {\bf 7}, 642 (2011)]. Here we predict that this kind of composite fermions may provide a realization of the quantum anomalous Hall effect by tuning the atom-atom interaction or the filling of the bosons in the mixture. We also…
We theoretically investigate the transport properties of cold bosonic atoms in a quasi one-dimensional triple-well potential that consists of two large outer wells, which act as microscopic source and drain reservoirs, and a small inner well, which represents a quantum-dot-like scattering region. Bias and gate "voltages" introduce a time-dependent tilt of the triple-well configuration, and are used to shift the energetic level of the inner well with respect to the outer ones. By means of exact diagonalization considering a total number of six atoms in the triple-well potential, we find diamond…
The dynamical properties of a one-dimensional system of two and three bosons escaping from an open potential well are studied in terms of the momentum distributions of particles. In the case of a two-boson system, it is shown that the single- and two-particle momentum distributions undergo a specific transition as the interaction strength is tuned through the point where tunneling switches from the pair tunneling to the sequential one. Characteristic features in the momentum spectra can be used to quantitatively determine the participation of specific decay processes. A corresponding analysis …
Motivated by recent advance in orbitally tuned Feshbach resonance experiments, we analyze the ground-state phase diagram and related low-energy excitation spectra of a d-wave interacting Bose gas. A two-channel model with d-wave symmetric interactions and background s-wave interactions is adopted to characterize the gas. The ground state is found to show three interesting phases: atomic, molecular, and atomic-molecular superfluidity. Remarkably differently from what was previously known in the p-wave case, the atomic superfluid is found to be momentum-independent in the present d-wave case. Bo…
We study the three-dimensional bosonic t-J model, i.e., the t-J model of "bosonic electrons" at finite temperatures. This model describes a system of cold bosonic atoms with two species in an optical lattice. The model is derived from the Hubbard model for very large on-site repulsive interaction between bosons of same species (hard-core nature) and also strong correlations between different species. The operator B_{xσ} for an atom at the site x with a two-component (pseudo-) spin σ(=1,2) is treated as a hard-core boson operator, and represented by a composite of two slave particles; a spinon …
The entanglement of vortices in a two-dimensional Bose-Hubbard model with artificial gauge fields is investigated using the exact diagonalization techniques. We propose an effective Hamiltonian for the spin-spin interactions between vortices responsible for this entanglement, and show that the entanglement can be detected through the quantum interference of the bosons in the vortex centers achieved using the Raman coupling and the quantum gas microscope. The strong bosonic coherence between the vortex centers originates from the charge-density wave order in the vortex core. It is robust agains…
We study the spatial correlations of strongly interacting bosons in a ground state, confined in two-dimensional square and three-dimensional cubic lattice. Using combined Bogoliubov method and the quantum rotor approach, we map the Hamiltonian of strongly interacting bosons onto U(1) phase action in order to calculate the atom-atom correlations decay along the principal axis and a diagonal of the lattice plane direction as a function of distance. Lower tunneling rates lead to quicker decays of the correlations, which character becomes exponential. Finally, correlation functions allow us to cal…
We study bosonic atoms with two internal states in artificial gauge potentials whose strengths are different for the two components. A series of topological phases for such systems is proposed using the composite fermion theory and the parton construction. It is found in exact diagonalization that some of the proposed states may be realized for simple contact interaction between bosons. The ground states and low-energy excitations of these states are modeled using trial wave functions. The effective field theories for these states are also constructed and reveal some interesting properties.
In a recent work, Murmann {\it et. al.} [Phys. Rev. Lett. {\bf114}, 080402 (2015)] have experimentally prepared and manipulated a double-well optical potential containing a pair of Fermi atoms as a possible building block of Hubbard model. Here, we carry out a detailed theoretical study on the properties of both fermionic and bosonic two-site Hubbard models with a pair of interacting atoms in a trap with a double-well structure along z-axis and a 2D harmonic confinement along the transverse directions. We consider fermions as of two-component type and bosons as of spinless as well as of two sp…
We derive an effective quantum Josephson array model for a weakly interacting one-dimensional condensate that is fragmented into weakly coupled puddles by a disorder potential. The distribution of coupling constants, obtained from first principles, indicate that weakly interacting bosons in a disorder potential undergo a superfluid insulator transition controlled by a strong randomness fixed point [Phys. Rev. Lett. 93, 150402 (2004)]. We compute renormalization group flows for concrete realizations of the disorder potential to facilitate finite size scaling of experimental results and allow co…
Trapping ultra-cold atoms in optical lattices provides a unique environment for investigating quantum phase transitions between strongly correlated superfluid and Mott insulator phases. One of the major complications in the analysis of experiments is establishing of criteria for identifying the superfluid phase. Sharp features occurring while entering ordered state have been recognized as a signature of superfluidity. In the present work it is shown that sharp peaks are not necessarily a reliable diagnostic of phase coherence in these systems. Using the combined Bogoliubov method and the quant…
The coupled equations which describe the temporal evolution of the Bose-Einstein condensed system are derived in the framework of nonequilibrium Thermo Field Dynamics. The key element is that they are not the naive assemblages of presumable equations, but are the self-consistent ones derived by appropriate renormalization conditions. While the order parameter is time-dependent, an explicit quasiparticle picture is constructed by a time-dependent expansion. Our formulation is valid even for the system with a unstable condensate, and describes the condensate decay caused by the Landau instabilit…
