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arXiv:cond-mat/0403746

On Quantum Bosonic Solids and Bosonic Superfluids

Zaira Nazario, David Santiago

Published Mar 31, 2004• 2 citations
arXivHTMLPDF

Abstract

We review the nature of superfluid ground states and the universality of their properties with emphasis to Bose Einstein Condensate systems in atomic physics. We then study the superfluid Mott transition in such systems. We find that there could be two types of Mott transitions and phases. One of them was described long ago and corresponds to suppression of Josephson tunneling within superfluids sitting at each well. On the other hand, the conditions of optical lattice BEC experiments are such that either the coherence length is longer than the interwell separation, or there is too small a number of bosons per well. This vitiates the existence of a superfluid order parameter within a well, and therefore of Josephson tunneling between wells. Under such conditions, there is a transition to a Mott phase which corresponds to suppression of individual boson tunneling among wells. This last transition is in general discontinuous and can happen for incommensurate values of bosons per site. If the coherence length is small enough and the number of bosons per site large enough, the transition studied in the earlier work will happen.

DOI
10.48550/arxiv.cond-mat/0403746

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Ultracold Bose gases as precise quantum simulators have emerged amongst the leaders in the current race  – a second quantum revolution  – toward the promise of unfathomable sensitivity, scope, and speed of a new era of technology. The only path leading to these advancements is through many-body descriptions, especially in regimes where interatomic interactions render many approximations incompatible with the physics. The research in this dissertation unlocks a piece of this mystery through investigations of many-body quantum tunneling of ultracold bosons in optical lattices. A key mechanism to characterizing the dynamics, matrix product state simulations equip the many-body toolbox with efficient optimization of large Hilbert spaces together with correlation and entropy measures that help clarify when semiclassical or mean-field approximations fail. In this thesis we obtain the following results. Macroscopic quantum tunneling escape of a Bose-Einstein condensate  – comprised of tens of thousands of 87Rb atoms  – from a single well, as portrayed through both experiment and theory, highlights non-exponential decay in the number of atoms trapped behind the barrier. Additionally, explicit symmetry breaking of a biperiodic optical lattice ring trap to a uniform one illustrates a critical symmetry-breaking strength at which the system transitions from a state of remembering to a state of forgetting its initial symmetry state; this symmetry memory indicates a new form of quantum dynamics that requires the quantum advantage for scaling up particle number and lattice sites. Extensive characterization of dynamical regimes in a bosonic Josephson junction  – underlaid by an optical lattice as described by the Bose-Hubbard model  – reveal substantial deviation of many body dynamics from the mean field or semiclassical predictions underlying the usual operating regime of Josephson junctions. Initial state population and phase yield insight into dynamic tunneling regimes of a quasi one-dimensional double well potential, through the Z2 spontaneous symmetry-breaking phase transition from Josephson oscillations to macroscopic self-trapping. We demonstrate that with increasing repulsive interaction strength, the U(1) superfluid-Mott insulator phase transition induces localized dynamics in the number density, such as particle-hole and soliton formation. Moreover, g^(2) correlations unveil a new dynamic regime  – the Fock flashlight. The new field of atomtronics  – or atomic circuits  – has emerged with many studies of weakly-interacting condensates. In contrast, and building on our work on many-body effects in the double wells underlying Josephson junctions, we present a proof-of-principle of a Mott-insulating atomtronic switch that requires strongly-interacting bosons. Through transient analysis, we reveal that hole conductance can be modulated via tuning interaction strength through a critical value, thus propelling the state to the next ``wedding cake'' layer of the Mott insulating structure. This critical interaction strength is a…

•Jan 1, 2018•0 citations
We review the nature of superfluid ground states and the universality of their properties with emphasis to Bose Einstein Condensate systems in atomic physics. We then study the superfluid Mott transition in such systems. We find that there could be two types of Mott transitions and phases. One of them was described long ago and corresponds to suppression of Josephson tunneling within superfluids sitting at each well. On the other hand, the conditions of optical lattice BEC experiments are such that either the coherence length is longer than the interwell separation, or there is too small a number of bosons per well. This vitiates the existence of a superfluid order parameter within a well, and therefore of Josephson tunneling between wells. Under such conditions, there is a transition to a Mott phase which corresponds to suppression of individual boson tunneling among wells. This last transition is in general discontinuous and can happen for incommensurate values of bosons per site. If the coherence length is small enough and the number of bosons per site large enough, the transition studied in the earlier work will happen.
We review the nature of superfluid ground states and the universality of their properties with emphasis to the Bose Einstein condensate (BEC) systems in atomic physics. We then study the superfluid Mott transition in such systems. We find that there could be two types of Mott transitions and phases. One of them was described long ago and corresponds to the suppression of Josephson tunneling within superfluids sitting at each well. On the other hand, the conditions of optical lattice BEC experiments are such that either the coherence length is longer than the interwell separation, or there is too small a number of bosons per well. This vitiates the existence of a superfluid order parameter within a well, and therefore of Josephson tunneling between wells. Under such conditions, there is a transition to a Mott phase which corresponds to the suppression of individual boson tunneling among wells. This last transition is in general discontinuous and can happen for incommensurate values of bosons per site. If the coherence length is small enough and the number of bosons per site is large enough, the transition studied in the earlier work will happen.
We study inter-well coherent quantum tunneling of Bose-Einstein condensates (BEC's) in optical lattices. Irrespective of whether the BEC is a superfluid in the whole lattice, it may or may not be a superfluid within each well of the lattice depending on whether the ratio of the well kinetic energy to the interaction energy is small or large. When the bosons in each well are superfluid, we have Josephson tunneling among the wells driven by the phase difference between the superfluids in the different wells. For typical lattice parameters the Josephson tunneling rate will be somewhat enhanced from the naive estimate of (tunneling energy scale)/ℏ/\hbar/ℏ. Whether it is enhanced or not will depend on lattice parameters, but it can never be zero. When the bosons in each well are not superfluid, there is coherent quantum tunneling of essentially free bosons between the wells. This tunneling is proportional to the boson number difference between the wells.
Confinement of atoms by laser technology has opened up a new field of physics. Following the realization of Bose– Einstein condensation (BEC) of bosonic atoms, fermionic atom systems and even boson–fermion mixture systems were successfully trapped and cooled. Application of a periodic potential, so called optical lattice, could also unveil interesting nature of the atoms. One of the interesting phenomena of the atoms on optical lattice is Mott transition. Although there is a long history of the study on bosons or fermions on lattice, coexistence of bosons and fermions on lattice is a rather new topic to study. In particular, we have little knowledge about strongly-correlated bosons and fermions on lattice. In our previous works we performed numerical simulations of Bose–Fermi mixtures to clarify the phase diagram and the effect of the confinement potential. When the total number of bosonic and fermionic atoms per site takes an integer value and interatomic interactions are sufficiently strong, the system would undergo Mott transition where the local atom density is fixed to the integer value. A characteristic of this Mott insulating phase is that a boson and fermion located next to each other can exchange their positions by going through a virtual doubly-occupied state with the atom exchange energy t ’ tbtf=Ubf where tb and tf are the hopping energy of the bosons and fermions respectively and Ubf denotes the on-site interaction between the boson and the fermion. Although there still remain a number of open questions on the Mott state of Bose–Fermi mixtures, the property of superfluid state of the strongly-correlated bosons and fermions has yet to be revealed. In this short note we would like to focus on strongly-correlated Bose–Fermi mixtures at commensurate filling in a three-dimensional periodical potential and see characteristic behaviors, if any, of the superfluid phase close to the phase boundary to the Mott insulating phase. In the following analysis we assume uniformity of the system and thus neglect the possibility of the emergence of so-called supersolid where superfluidity and structural long-range order coexist. For simplicity we ignore all the internal degree of freedom of the atoms and the influence of the trap potential which in fact creates a nonuniform density profile of the bosons and fermions. For the system at commensurate filling on optical lattice, we assume that the interatomic interactions are weak enough to avoid formation of Mott state but strong enough to allow us to expect that there are only few empty or doublyoccupied sites and most sites are singly occupied. Namely we analyze the system that stays in a superfluid phase but lies close to the boundary to the Mott phase. Since a boson and fermion located next to each other can exchange their positions as stated above, the energy of the superfluid state of the mixture system is given mostly by the kinetic energy of the bosons and fermions exchanging their positions. We therefore express the Hamiltonian in the following form, ignoring the kinetic energy of the atoms at the empty sites and the interaction energy at the doubly-occupied sites:
Motivated by recent experiments on trapped ultracold bosonic atoms in an optical lattice potential, we consider the nonequilibrium dynamic properties of such bosonic systems for a number of experimentally relevant situations. When the number of bosons per lattice site is large, there is a wide parameter regime where the effective boson interactions are strong, but the ground state remains a superfluid (and not a Mott insulator): we describe the conditions under which the dynamics in this regime can be described by a discrete Gross-Pitaevskii equation. We describe the evolution of the phase coherence after the system is initially prepared in a Mott insulating state, and then allowed to evolve after a sudden change in parameters places it in a regime with a superfluid ground state. We also consider initial conditions with a ``\ensuremath{\pi} phase'' imprint on a superfluid ground state (i.e., the initial phases of neighboring wells differ by \ensuremath{\pi}), and discuss the subsequent appearance of the density wave order and ``Schr\"odinger cat,'' i.e., macroscopic quantum interference, states.
Abstract The physics of bosonic atoms in optical lattices is described. Starting from the basic experimental tools available to create such systems, the chapter introduces a simple model (known as the Bose—Hubbard model) for such a system. A mean-field type picture is developed to determine the basic character of the superfluid and Mott-insulating phases, and the physical conditions under which each should arise. A number of experimental methods are outlined to detect the properties of the gas. The fact that two thermodynamic ground states exist at zero temperature with different types of order implies the existence of a quantum phase transition. The behavior of the gas near this transition is described using an entirely different framework—quantum criticality—formed around the concepts of scaling symmetry and the renormalization group.
Ultracold Bose gases as precise quantum simulators have emerged amongst the leaders in the current race  – a second quantum revolution  – toward the promise of unfathomable sensitivity, scope, and speed of a new era of technology. The only path leading to these advancements is through many-body descriptions, especially in regimes where interatomic interactions render many approximations incompatible with the physics. The research in this dissertation unlocks a piece of this mystery through investigations of many-body quantum tunneling of ultracold bosons in optical lattices. A key mechanism to characterizing the dynamics, matrix product state simulations equip the many-body toolbox with efficient optimization of large Hilbert spaces together with correlation and entropy measures that help clarify when semiclassical or mean-field approximations fail. In this thesis we obtain the following results. Macroscopic quantum tunneling escape of a Bose-Einstein condensate  – comprised of tens of thousands of 87Rb atoms  – from a single well, as portrayed through both experiment and theory, highlights non-exponential decay in the number of atoms trapped behind the barrier. Additionally, explicit symmetry breaking of a biperiodic optical lattice ring trap to a uniform one illustrates a critical symmetry-breaking strength at which the system transitions from a state of remembering to a state of forgetting its initial symmetry state; this symmetry memory indicates a new form of quantum dynamics that requires the quantum advantage for scaling up particle number and lattice sites. Extensive characterization of dynamical regimes in a bosonic Josephson junction  – underlaid by an optical lattice as described by the Bose-Hubbard model  – reveal substantial deviation of many body dynamics from the mean field or semiclassical predictions underlying the usual operating regime of Josephson junctions. Initial state population and phase yield insight into dynamic tunneling regimes of a quasi one-dimensional double well potential, through the Z2 spontaneous symmetry-breaking phase transition from Josephson oscillations to macroscopic self-trapping. We demonstrate that with increasing repulsive interaction strength, the U(1) superfluid-Mott insulator phase transition induces localized dynamics in the number density, such as particle-hole and soliton formation. Moreover, g^(2) correlations unveil a new dynamic regime  – the Fock flashlight. The new field of atomtronics  – or atomic circuits  – has emerged with many studies of weakly-interacting condensates. In contrast, and building on our work on many-body effects in the double wells underlying Josephson junctions, we present a proof-of-principle of a Mott-insulating atomtronic switch that requires strongly-interacting bosons. Through transient analysis, we reveal that hole conductance can be modulated via tuning interaction strength through a critical value, thus propelling the state to the next ``wedding cake'' layer of the Mott insulating structure. This critical interaction strength is a…