Developing a theoretical framework to access the quantum phases of itinerant bosons or fermions in two dimensions that exhibit singular structure along surfaces in momentum space but have no quasiparticle description remains a central challenge in the field of strongly correlated physics. In this paper we propose that distinctive signatures of such two-dimensional (2D) strongly correlated phases will be manifest in quasi-one-dimensional `` $N$ -leg ladder'' systems. Characteristic of each parent 2D quantum liquid would be a precise pattern of one-dimensional (1D) gapless modes on the $N$ -leg ladder. These signatures could be potentially exploited to approach the 2D phases from controlled numerical and analytical studies in quasi-one-dimension. As a first step we explore itinerant-boson models with a frustrating ring-exchange interaction on the two-leg ladder, searching for signatures of the recently proposed two-dimensional $d$ -wave-correlated Bose liquid (DBL) phase. A combination of exact diagonalization, density-matrix renormalization-group, variational Monte Carlo, and bosonization analysis of a quasi-1D gauge theory provide compelling evidence for the existence of an unusual strong-coupling phase of bosons on the two-leg ladder, which can be understood as a descendant of the two-dimensional DBL. We suggest several generalizations to quantum spin and electron Hamiltonians on ladders, which could likewise reveal fingerprints of such 2D non-Fermi-liquid phases.Developing a theoretical framework to access the quantum phases of itinerant bosons or fermions in two dimensions that exhibit singular structure along surfaces in momentum space but have no quasiparticle description remains a central challenge in the field of strongly correlated physics. In this paper we propose that distinctive signatures of such two-dimensional (2D) strongly correlated phases will be manifest in quasi-one-dimensional ``$N$-leg ladder'' systems. Characteristic of each parent 2D quantum liquid would be a precise pattern of one-dimensional (1D) gapless modes on the $N$-leg ladder. These signatures could be potentially exploited to approach the 2D phases from controlled numerical and analytical studies in quasi-one-dimension. As a first step we explore itinerant-boson models with a frustrating ring-exchange interaction on the two-leg ladder, searching for signatures of the recently proposed two-dimensional $d$-wave-correlated Bose liquid (DBL) phase. A combination of exact diagonalization, density-matrix renormalization-group, variational Monte Carlo, and bosonization analysis of a quasi-1D gauge theory provide compelling evidence for the existence of an unusual strong-coupling phase of bosons on the two-leg ladder, which can be understood as a descendant of the two-dimensional DBL. We suggest several generalizations to quantum spin and electron Hamiltonians on ladders, which could likewise reveal fingerprints of such 2D non-Fermi-liquid phases.

arXiv:0805.0255Physical Review BAug 26, 200852 citations

Interacting bosonic fields

Jan Dereziński, Christian Gérard

Cambridge University Press eBooksNov 4, 20220 citations

Generalized Spin-Boson model and its application to dissipative Bose-Josephson Junction

Sudip Sinha, Supervisor Dr. Subhasis Sinha

We investigate the effect of dissipation in a Bose Josephson junction (BJJ) coupled to bath of bosons at two sites as an application of the generalized spin-boson model. Apart from the dynamical transition due to repulsive interactions, the BJJ undergoes a quantum phase transition by increasing the coupling strength with the bath modes. We analyze this system by mapping to an equivalent spin model coupled to the bosonic modes. The excitation energies and fluctuation of number imbalance are obtained within Holstein-Primakoff approximation, which exhibits vanishing of energy gap and enhanced quantum fluctuations at the critical coupling. We study the dynamics of BJJ using time-dependent variational method and analyze stability of different types of steady states. As a special case, we study in details the phase space dynamics of BJJ coupled to a single-mode, which reveals diffusive and incoherent behaviour with increasing coupling to the bath mode. The dynamical steady states corresponding to the Pi-oscillation and self-trapped state become unstable in the region where their oscillation frequencies are in resonance with the bath modes. We investigate the time evolution of number imbalance and relative phase in presence of Ohmic bath with Gaussian noise to incorporate thermal fluctuations. Apart from the damping of Josephson oscillations and transition to symmetry broken state for strong coupling, we observe the decay of Pi-oscillation and self-trapped state to the ground state as a result of dissipation. Variation of phase fluctuation with temperature of the bath shows similar behaviour as observed in the experiments.We investigate the effect of dissipation in a Bose Josephson junction (BJJ) coupled to bath of bosons at two sites as an application of the generalized spin-boson model. Apart from the dynamical transition due to repulsive interactions, the BJJ undergoes a quantum phase transition by increasing the coupling strength with the bath modes. We analyze this system by mapping to an equivalent spin model coupled to the bosonic modes. The excitation energies and fluctuation of number imbalance are obtained within Holstein-Primakoff approximation, which exhibits vanishing of energy gap and enhanced quantum fluctuations at the critical coupling. We study the dynamics of BJJ using time-dependent variational method and analyze stability of different types of steady states. As a special case, we study in details the phase space dynamics of BJJ coupled to a single-mode, which reveals diffusive and incoherent behaviour with increasing coupling to the bath mode. The dynamical steady states corresponding to the Pi-oscillation and self-trapped state become unstable in the region where their oscillation frequencies are in resonance with the bath modes. We investigate the time evolution of number imbalance and relative phase in presence of Ohmic bath with Gaussian noise to incorporate thermal fluctuations. Apart from the damping of Josephson oscillations and transition to symmetry broken state for strong coupling, we observe the decay of Pi-oscillation and self-trapped state to the ground state as a result of dissipation. Variation of phase fluctuation with temperature of the bath shows similar behaviour as observed in the experiments.

May 1, 20190 citations

Phase-space analysis of bosonic spontaneous emission

M. K. Olsen, Lev I. Plimak, S. Rebić +1 more

arXiv:quant-ph/0505011Optics CommunicationsJul 2, 200515 citations

Coherence behavior of strongly coupled bosonic modes

Jucelino Ferreira de Sousa, Carlos H. S. Vieira, Jonas F. G. Santos +1 more

We study the effect of the intermode coupling in the generation of coherence when two bosonic modes are bilinearly coupled. We consider the case for which the two modes are weakly coupled and the rotating-wave approximation (RWA) applies and the case for which they are strongly coupled and the RWA does not apply. Then, in the regime of validity of the RWA, there is no coherence generation solely due to squeezing effects, which means there is an exchange of excitation between the modes and negligible squeezing. On the other hand, if the two modes are strongly coupled coherence is generated by the squeezing interaction. For the system of two bosonic modes weakly coupled with a Markovian bath at temperature $T$ the coherence decreases with $T$ . In general, when both kinds of couplings (exchange of excitation and squeezing) are turned on the exchange of excitation contributes to generating more coherence in comparison with a purely squeezing coupling. Thus, the coherence decreases more slowly with the temperature when both couplings are present. Finally, we explore the case when only one of the two coupled modes interacts with a Markovian bath while the other one remains free from the environment. We observe that the intermode coupling induces oscillations in the coherence and fidelity dynamics similar to the behavior for the coupling with a non-Markovian environment.We study the effect of the intermode coupling in the generation of coherence when two bosonic modes are bilinearly coupled. We consider the case for which the two modes are weakly coupled and the rotating-wave approximation (RWA) applies and the case for which they are strongly coupled and the RWA does not apply. Then, in the regime of validity of the RWA, there is no coherence generation solely due to squeezing effects, which means there is an exchange of excitation between the modes and negligible squeezing. On the other hand, if the two modes are strongly coupled coherence is generated by the squeezing interaction. For the system of two bosonic modes weakly coupled with a Markovian bath at temperature $T$ the coherence decreases with $T$. In general, when both kinds of couplings (exchange of excitation and squeezing) are turned on the exchange of excitation contributes to generating more coherence in comparison with a purely squeezing coupling. Thus, the coherence decreases more slowly with the temperature when both couplings are present. Finally, we explore the case when only one of the two coupled modes interacts with a Markovian bath while the other one remains free from the environment. We observe that the intermode coupling induces oscillations in the coherence and fidelity dynamics similar to the behavior for the coupling with a non-Markovian environment.

arXiv:2208.10649Physical Review ASep 1, 20225 citations

Weakly-Bound Bosonic States in the Strongly Interacting Regime

Javier von Stecher

Bulletin of the American Physical SocietyJun 14, 20110 citations

N

-leg ladder'' systems. Characteristic of each parent 2D quantum liquid would be a precise pattern of one-dimensional (1D) gapless modes on the

N

-leg ladder. These signatures could be potentially exploited to approach the 2D phases from controlled numerical and analytical studies in quasi-one-dimension. As a first step we explore itinerant-boson models with a frustrating ring-exchange interaction on the two-leg ladder, searching for signatures of the recently proposed two-dimensional

d

-wave-correlated Bose liquid (DBL) phase. A combination of exact diagonalization, density-matrix renormalization-group, variational Monte Carlo, and bosonization analysis of a quasi-1D gauge theory provide compelling evidence for the existence of an unusual strong-coupling phase of bosons on the two-leg ladder, which can be understood as a descendant of the two-dimensional DBL. We suggest several generalizations to quantum spin and electron Hamiltonians on ladders, which could likewise reveal fingerprints of such 2D non-Fermi-liquid phases.

T

the coherence decreases with

T

. In general, when both kinds of couplings (exchange of excitation and squeezing) are turned on the exchange of excitation contributes to generating more coherence in comparison with a purely squeezing coupling. Thus, the coherence decreases more slowly with the temperature when both couplings are present. Finally, we explore the case when only one of the two coupled modes interacts with a Markovian bath while the other one remains free from the environment. We observe that the intermode coupling induces oscillations in the coherence and fidelity dynamics similar to the behavior for the coupling with a non-Markovian environment.