Transport and Entanglement Generation in the Bose-Hubbard Model

We study entanglement generation via particle transport across a one-dimensional system described by the Bose-Hubbard Hamiltonian. We analyze how the competition between interactions and tunneling affects transport properties and the creation of entanglement in the occupation number basis. Alternatively, we propose to use spatially delocalized quantum bits, where a quantum bit is defined by the presence of a particle either in a site or in the adjacent one. Our results can serve as a guidance for future experiments to characterize entanglement of ultracold gases in one-dimensional optical lattices.We study entanglement generation via particle transport across a one-dimensional system described by the Bose-Hubbard Hamiltonian. We analyze how the competition between interactions and tunneling affects transport properties and the creation of entanglement in the occupation number basis. Alternatively, we propose to use spatially delocalized quantum bits, where a quantum bit is defined by the presence of a particle either in a site or in the adjacent one. Our results can serve as a guidance for future experiments to characterize entanglement of ultracold gases in one-dimensional optical lattices.

arXiv:quant-ph/0703177Journal of Physics A Mathematical and TheoreticalJun 27, 200714 citations

Genuine multipartite entanglement in a one-dimensional Bose-Hubbard model with frustrated hopping

Sudipto Singha Roy, Leon Carl, Philipp Hauke

Frustration and quantum entanglement are two exotic quantum properties in quantum many-body systems. However, despite several efforts, an exact relationship between them remains elusive. In this work, we explore the relationship between frustration and quantum entanglement in a physical model describing strongly correlated ultracold bosonic atoms in optical lattices. In particular, we consider the one-dimensional Bose-Hubbard model comprising both nearest-neighbor ( ${t}_{1}$ ) and frustrated next-nearest neighbor ( ${t}_{2}$ ) hoppings and examine how the interplay of on-site interaction ( $U$ ) and hoppings results in different quantum correlations dominating the ground state of the system. We then analyze the behavior of quantum entanglement in the model. In particular, we compute genuine multipartite entanglement as quantified through the generalized geometric measure and make a comparative study with bipartite entanglement and other relevant order parameters. We observe that genuine multipartite entanglement has a very rich behavior throughout the considered parameter regime and frustration does not necessarily favor generating a high amount of it. Moreover, we show that in the region with strong quantum fluctuations, the particles remain highly delocalized in all momentum modes and share a very low amount of both bipartite and multipartite entanglement. Our work illustrates the necessity to give separate attention to dominating ordering behavior and quantum entanglement in the ground state of strongly correlated systems.Frustration and quantum entanglement are two exotic quantum properties in quantum many-body systems. However, despite several efforts, an exact relationship between them remains elusive. In this work, we explore the relationship between frustration and quantum entanglement in a physical model describing strongly correlated ultracold bosonic atoms in optical lattices. In particular, we consider the one-dimensional Bose-Hubbard model comprising both nearest-neighbor (${t}_{1}$) and frustrated next-nearest neighbor (${t}_{2}$) hoppings and examine how the interplay of on-site interaction ($U$) and hoppings results in different quantum correlations dominating the ground state of the system. We then analyze the behavior of quantum entanglement in the model. In particular, we compute genuine multipartite entanglement as quantified through the generalized geometric measure and make a comparative study with bipartite entanglement and other relevant order parameters. We observe that genuine multipartite entanglement has a very rich behavior throughout the considered parameter regime and frustration does not necessarily favor generating a high amount of it. Moreover, we show that in the region with strong quantum fluctuations, the particles remain highly delocalized in all momentum modes and share a very low amount of both bipartite and multipartite entanglement. Our work illustrates the necessity to give separate attention to dominating ordering behavior and quantum entanglement in the ground state of strongly correlated systems.

arXiv:2209.08815Physical review. B./Physical review. BNov 29, 202211 citations

Bose–Hubbard model with occupation-dependent parameters

Omjyoti Dutta, André Eckardt, Philipp Hauke +2 more

We study the ground-state properties of ultracold bosons in an optical lattice in the regime of strong interactions. The system is described by a non-standard Bose–Hubbard model with both occupation-dependent tunneling and on-site interaction. We find that for sufficiently strong coupling, the system features a phase transition from a Mott insulator with one particle per site to a superfluid of spatially extended particle pairs living on top of the Mott background—instead of the usual transition to a superfluid of single particles/holes. Increasing the interaction further, a superfluid of particle pairs localized on a single site (rather than being extended) on top of the Mott background appears. This happens at the same interaction strength where the Mott-insulator phase with two particles per site is destroyed completely by particle–hole fluctuations for arbitrarily small tunneling. In another regime, characterized by weak interaction but high occupation numbers, we observe a dynamical instability in the superfluid excitation spectrum. The new ground state is a superfluid, forming a two-dimensional (2D) slab, localized along one spatial direction that is chosen spontaneously.We study the ground-state properties of ultracold bosons in an optical lattice in the regime of strong interactions. The system is described by a non-standard Bose–Hubbard model with both occupation-dependent tunneling and on-site interaction. We find that for sufficiently strong coupling, the system features a phase transition from a Mott insulator with one particle per site to a superfluid of spatially extended particle pairs living on top of the Mott background—instead of the usual transition to a superfluid of single particles/holes. Increasing the interaction further, a superfluid of particle pairs localized on a single site (rather than being extended) on top of the Mott background appears. This happens at the same interaction strength where the Mott-insulator phase with two particles per site is destroyed completely by particle–hole fluctuations for arbitrarily small tunneling. In another regime, characterized by weak interaction but high occupation numbers, we observe a dynamical instability in the superfluid excitation spectrum. The new ground state is a superfluid, forming a two-dimensional (2D) slab, localized along one spatial direction that is chosen spontaneously.

arXiv:1009.1313New Journal of PhysicsFeb 9, 201159 citations

Many-body localization in the Bose-Hubbard model: Evidence for mobility edge

Ruixiao Yao, Jakub Zakrzewski

Motivated by recent experiments on interacting bosons in a quasi-one-dimensional optical lattice [M. Rispoli et al., Nature (London) 573, 385 (2019)], we analyze theoretically properties of the system in the crossover between delocalized and localized regimes. Comparison of time dynamics for uniform and density-wave-like initial states enables a demonstration of the existence of the mobility edge. To this end we define a different observable, the mean speed of transport at long times. It gives us an efficient estimate of the critical disorder for the crossover. We also show that the mean velocity growth of occupation fluctuations close to the edges of the system carries similar information. Using the quantum quench procedure, we show that it is possible to probe the mobility edge for different energies.Motivated by recent experiments on interacting bosons in a quasi-one-dimensional optical lattice [M. Rispoli et al., Nature (London) 573, 385 (2019)], we analyze theoretically properties of the system in the crossover between delocalized and localized regimes. Comparison of time dynamics for uniform and density-wave-like initial states enables a demonstration of the existence of the mobility edge. To this end we define a different observable, the mean speed of transport at long times. It gives us an efficient estimate of the critical disorder for the crossover. We also show that the mean velocity growth of occupation fluctuations close to the edges of the system carries similar information. Using the quantum quench procedure, we show that it is possible to probe the mobility edge for different energies.

arXiv:2002.00381Physical review. B./Physical review. BJul 21, 202024 citations

Atomic Bose-Hubbard Systems with Single-Particle Control

Philipp M. Preiss

Experiments with ultracold atoms in optical lattices provide outstanding opportunities to realize exotic quantum states due to a high degree of tunability and control. In this thesis, I present experiments that extend this control from global parameters to the level of individual particles. \n\nUsing a quantum gas microscope for 87Rb, we have developed a single-site addressing scheme based on digital amplitude holograms. The system self-corrects for aberrations in the imaging setup and creates arbitrary beam profiles. We are thus able to shape optical potentials on the scale of single lattice sites and control the dynamics of individual atoms. \n\nWe study the role of quantum statistics and interactions in the Bose-Hubbard model on the fundamental level of two particles. Bosonic quantum statistics are apparent in the Hong-Ou-Mandel interference of massive particles, which we observe in tailored double-well potentials. These underlying statistics, in combination with tunable repulsive interactions, dominate the dynamics in single- and two-particle quantum walks. We observe highly coherent position-space Bloch oscillations, bosonic bunching in Hanbury Brown-Twiss interference and the fermionization of strongly interacting bosons.\n\nMany-body states of indistinguishable quantum particles are characterized by large-scale spatial entanglement, which is difficult to detect in itinerant systems. Here, we extend the concept of Hong-Ou-Mandel interference from individual particles to many-body states to directly quantify entanglement entropy. We perform collective measurements on two copies of a quantum state and detect entanglement entropy through many-body interference. We measure the second order Rényi entropy in small Bose-Hubbard systems and detect the buildup of spatial entanglement across the superfluid-insulator transition.\n\nOur experiments open new opportunities for the single-particle-resolved preparation and characterization of many-body quantum states.Experiments with ultracold atoms in optical lattices provide outstanding opportunities to realize exotic quantum states due to a high degree of tunability and control. In this thesis, I present experiments that extend this control from global parameters to the level of individual particles. \n\nUsing a quantum gas microscope for 87Rb, we have developed a single-site addressing scheme based on digital amplitude holograms. The system self-corrects for aberrations in the imaging setup and creates arbitrary beam profiles. We are thus able to shape optical potentials on the scale of single lattice sites and control the dynamics of individual atoms. \n\nWe study the role of quantum statistics and interactions in the Bose-Hubbard model on the fundamental level of two particles. Bosonic quantum statistics are apparent in the Hong-Ou-Mandel interference of massive particles, which we observe in tailored double-well potentials. These underlying statistics, in combination with tunable repulsive interactions, dominate the dynamics in single- and two-particle quantum walks. We observe highly coherent position-space Bloch oscillations, bosonic bunching in Hanbury Brown-Twiss interference and the fermionization of strongly interacting bosons.\n\nMany-body states of indistinguishable quantum particles are characterized by large-scale spatial entanglement, which is difficult to detect in itinerant systems. Here, we extend the concept of Hong-Ou-Mandel interference from individual particles to many-body states to directly quantify entanglement entropy. We perform collective measurements on two copies of a quantum state and detect entanglement entropy through many-body interference. We measure the second order Rényi entropy in small Bose-Hubbard systems and detect the buildup of spatial entanglement across the superfluid-insulator transition.\n\nOur experiments open new opportunities for the single-particle-resolved preparation and characterization of many-body quantum states.

Dec 14, 20150 citations

Tunneling of ultracold Bose gases in multiple wells

R. Paredes

We study the dynamics of an ultracold gas of interacting bosons confined in a one-dimensional potential composed of $n$ wells. We derive an effective $N$ -particle Hamiltonian for this system that describes the tunneling of particles between adjacent wells and that includes the interactions among the particles within the same well. The problem is discussed in the light of current research on optical lattices. We demonstrate that the effective Hamiltonian gives the possibility of studying the transition from an ideal insulator to a real conductor when the parameters that modulate the interaction and the tunneling of the particles are varied. To show this we numerically solve Schr\"odinger equation for the case of $n=3$ wells. We find that for a given number of particles it is possible to establish a weak- and a strong-interaction regime. In the limit of strong interaction the tunneling term can be neglected. One important result in our analysis is that in the weak-interaction regime the system reaches a stationary state as a result of the loss of coherence in the transport of particles through the wells.We study the dynamics of an ultracold gas of interacting bosons confined in a one-dimensional potential composed of $n$ wells. We derive an effective $N$-particle Hamiltonian for this system that describes the tunneling of particles between adjacent wells and that includes the interactions among the particles within the same well. The problem is discussed in the light of current research on optical lattices. We demonstrate that the effective Hamiltonian gives the possibility of studying the transition from an ideal insulator to a real conductor when the parameters that modulate the interaction and the tunneling of the particles are varied. To show this we numerically solve Schr\"odinger equation for the case of $n=3$ wells. We find that for a given number of particles it is possible to establish a weak- and a strong-interaction regime. In the limit of strong interaction the tunneling term can be neglected. One important result in our analysis is that in the weak-interaction regime the system reaches a stationary state as a result of the loss of coherence in the transport of particles through the wells.

Physical Review AMar 17, 200614 citations

{t}_{1}

) and frustrated next-nearest neighbor (

{t}_{2}

) hoppings and examine how the interplay of on-site interaction (

U

) and hoppings results in different quantum correlations dominating the ground state of the system. We then analyze the behavior of quantum entanglement in the model. In particular, we compute genuine multipartite entanglement as quantified through the generalized geometric measure and make a comparative study with bipartite entanglement and other relevant order parameters. We observe that genuine multipartite entanglement has a very rich behavior throughout the considered parameter regime and frustration does not necessarily favor generating a high amount of it. Moreover, we show that in the region with strong quantum fluctuations, the particles remain highly delocalized in all momentum modes and share a very low amount of both bipartite and multipartite entanglement. Our work illustrates the necessity to give separate attention to dominating ordering behavior and quantum entanglement in the ground state of strongly correlated systems.

We study the dynamics of an ultracold gas of interacting bosons confined in a one-dimensional potential composed of

n

wells. We derive an effective

N

-particle Hamiltonian for this system that describes the tunneling of particles between adjacent wells and that includes the interactions among the particles within the same well. The problem is discussed in the light of current research on optical lattices. We demonstrate that the effective Hamiltonian gives the possibility of studying the transition from an ideal insulator to a real conductor when the parameters that modulate the interaction and the tunneling of the particles are varied. To show this we numerically solve Schr\"odinger equation for the case of

n=3

wells. We find that for a given number of particles it is possible to establish a weak- and a strong-interaction regime. In the limit of strong interaction the tunneling term can be neglected. One important result in our analysis is that in the weak-interaction regime the system reaches a stationary state as a result of the loss of coherence in the transport of particles through the wells.