Bosonic Bath Research Articles

Engineering impurity Bell states through coupling with a quantum bath

We theoretically demonstrate the feasibility of creating Bell states in multicomponent ultracold atomic gases by solely using the ability to control the interparticle interactions via Feshbach resonances. For this we consider two distinguishable impurities immersed in an atomic background cloud of a few bosons, with the entire system being confined in a one-dimensional harmonic trap. By analyzing the numerically obtained ground states we demonstrate that the two impurities can form spatially entangled bipolaron states due to mediated interactions from the bosonic bath. Our analysis is based on calculating the correlations between the two impurities in a two-mode basis, which is experimentally accessible by measuring the particle positions in the left or right sides of the trap. While interspecies interactions are crucial in order to create the strongly entangled impurity states, they can also inhibit correlations depending on the ordering of the impurities and three-body impurity-bath correlations. We show how these drawbacks can be mitigated by manipulating the properties of the bath, namely its size, mass, and intraspecies interactions, allowing one to create impurity Bell states over a wide range of impurity-impurity interactions. Published by the American Physical Society 2024

Self-oscillating open quantum systems

Evolution of occupation number is studied for a bosonic oscillator (with one and two degrees of freedom) linearly fully coupled to fermionic and bosonic heat baths. The lack of equilibrium in this oscillator is discussed in the light of the creation of an energy source. The connection of such a system with known nonlinear self-oscillating systems is shown.

Universal correlation between H-linear magnetoresistance and T-linear resistivity in high-temperature superconductors

The signature feature of the ‘strange metal’ state of high-Tc cuprates—its linear-in-temperature resistivity—has a coefficient α1 that correlates with Tc, as expected were α1 derived from scattering off the same bosonic fluctuations that mediate pairing. Recently, an anomalous linear-in-field magnetoresistance (=γ1H) has also been observed, but only over a narrow doping range, leaving its relation to the strange metal state and to the superconductivity unclear. Here, we report in-plane magnetoresistance measurements on three hole-doped cuprate families spanning a wide range of temperatures, magnetic field strengths and doping. In contrast to expectations from Boltzmann transport theory, γ1 is found to correlate universally with α1. A phenomenological model incorporating real-space inhomogeneity is proposed to explain this correlation. Within this picture, superconductivity in hole-doped cuprates is governed not by the strength of quasiparticle interactions with a bosonic bath, but by the concentration of strange metallic carriers.

Harnessing coherence generation for precision single- and two-qubit quantum thermometry

Quantum probes, such as single- and two-qubit probes, can accurately measure the temperature of a bosonic bath. The current investigation assesses the precision of the temperature estimate by using quantum Fisher information and the accompanying quantum signal-to-noise ratio. Employing an ancilla as a mediator between the probe and the bath improves thermometric sensitivity by transmitting temperature information into the probe qubit's coherences. In addition, we analyze two interacting qubits that were initially entangled or separated as quantum probes for various environmental configurations. Our findings show that increased precision is gained when the probe approaches its steady state, which is determined by the coupling between the two qubits. Furthermore, we can obtain high-efficiency temperature estimation for any low temperature by changing the interaction between the two qubits. Published by the American Physical Society 2024

Induced magnetization in anisotropic environment

The non-Markovian dynamics of a two-dimensional charged harmonic oscillator linearly coupled to a neutral bosonic heat bath is investigated in a linear-polarized electric field. The analytical expressions for the time-dependent and asymptotic magnetic moment are derived for the Markovian and non-Markovian dynamics. It is predicted that the liner-polarized electric field generates strong orbital currents and magnetization in a symmetric harmonic oscillator embedded into anisotropic heat bath. The role of the mixed dissipative kernel in magnetization is analyzed.

Half Landau–Zener ramp to a quantum phase transition in a dissipative single spin model

We study the dynamics of a single spin coupled to a bosonic bath at zero temperature driven by a ramp of the bias field. A single spin coupled to a bosonic sub-Ohmic bath exhibits a quantum phase transition at a certain strength of spin-boson coupling. When the bias field is ramped from a large value to zero at this critical coupling strength, the system initialized at the ground state ends up with a finite magnetization due to the critical slowing down near the transition. On the basis of the pulse-impulse approximation, we derive a scaling law between the residual magnetization and the ramp speed. The obtained scaling relation is examined using a numerical simulation based on the tensor network. The data are in favor of the scaling law to hold. We discuss the demonstration of our theoretical results by means of quantum simulation using the quantum annealer.Graphical abstract

Bound impurities in a one-dimensional Bose lattice gas: Low-energy properties and quench-induced dynamics

We study two mobile bosonic impurities immersed in a one-dimensional optical lattice and interacting with a bosonic bath. We employ the exact diagonalization method for small periodic lattices to study stationary properties and dynamics. We consider the branch of repulsive interactions that induce the formation of bound impurities, akin to the bipolaron problem. A comprehensive study of ground-state and low-energy properties is presented, including an examination of the interaction strengths which induce the formation of a bound dimer of impurities. We also study the dynamics induced after an interaction quench to examine the stability of the bound dimers. We reveal that after large interaction quenches from strong to weak interactions the system can show large oscillations over time with revivals of the dimer states. We find that the oscillations are driven by selected eigenstates with phase-separated configurations.

Entanglement and correlations in an exactly-solvable model of a Bose–Einstein condensate in a cavity

An exactly solvable model of a trapped interacting Bose–Einstein condensate (BEC) coupled in the dipole approximation to a quantized light mode in a cavity is presented. The model can be seen as a generalization of the harmonic-interaction model for a trapped BEC coupled to a bosonic bath. After obtaining the ground-state energy and wavefunction in closed form, we focus on computing the correlations in the system. The reduced one-particle density matrices of the bosons and the cavity are constructed and diagonalized analytically, and the von Neumann entanglement entropy of the BEC and the cavity is also expressed explicitly as a function of the number and mass of the bosons, frequencies of the trap and cavity, and the cavity-boson coupling strength. The results allow one to study the impact of the cavity on the bosons and vice versa on an equal footing. As an application we investigate a specific case of basic interest for itself, namely, non-interacting bosons in a cavity. We find that both the bosons and the cavity develop correlations in a complementary manner while increasing the coupling between them. Whereas the cavity wavepacket broadens in Fock space, the BEC density saturates in real space. On the other hand, while the cavity depletion saturates, and hence does the BEC-cavity entanglement entropy, the BEC becomes strongly correlated and eventually increasingly fragmented. The latter phenomenon implies single-trap fragmentation of otherwise ideal bosons, where their induced long-range interaction is mediated by the cavity. Finally, as a complimentary investigation, the mean-field equations for the BEC-cavity system are solved analytically as well, and the breakdown of mean-field theory for the cavity and the bosons with increasing coupling is discussed. Further applications are envisaged.

Diagnosing Thermalization Dynamics of Non-Hermitian Quantum Systems via GKSL Master Equations

Abstract The application of the eigenstate thermalization hypothesis to non-Hermitian quantum systems has become one of the most important topics in dissipative quantum chaos, recently giving rise to intense debates. The process of thermalization is intricate, involving many time-evolution trajectories in the reduced Hilbert space of the system. By considering two different expansion forms of the density matrices adopted in the biorthogonal and right-state time evolutions, we derive two versions of the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) master equations describing the non-Hermitian systems coupled to a bosonic heat bath in thermal equilibrium. By solving the equations, we identify a sufficient condition for thermalization under both time evolutions, resulting in Boltzmann biorthogonal and right-eigenstate statistics, respectively. This finding implies that the recently proposed biorthogonal random matrix theory needs an appropriate revision. Moreover, we exemplify the precise dynamics of thermalization and thermodynamic properties with test models.

Synthesizing and multiplexing autonomous quantum coherences

Quantum coherence is a crucial prerequisite for quantum technologies. Therefore, the robust generation, as autonomous as possible, of quantum coherence remains the essential problem for developing this field. We consider a method of synthesizing and multiplexing quantum coherence from spin systems without any direct drives only coupled to bosonic baths. The previous studies in this field have demonstrated that a back-action of the bath to the spin subsystem is important to generate it, however, it simultaneously gives significant limits to the generated coherence. We propose a viable approach with the bosonic bath that allows overcoming these limits by avoiding the destructive effect of the back-action processes. Using this approach, we suggest an advanced synthesis of the quantum coherence non-perturbatively in the spin-boson coupling parameters of multiple bosonic baths to increase and multiplex it for upcoming proof-of-principle experiments.

Bath-induced interactions and transient dynamics in open quantum systems at strong coupling: Effective Hamiltonian approach.

Understanding the dynamics of dissipative quantum systems, particularly beyond the weak coupling approximation, is central to various quantum applications. While numerically exact methods provide accurate solutions, they often lack the analytical insight provided by theoretical approaches. In this study, we employ the recently developed method dubbed the effective Hamiltonian theory to understand the dynamics of system-bath configurations without resorting to a perturbative description of the system-bath coupling energy. Through a combination of mapping steps and truncation, the effective Hamiltonian theory offers both analytical insights into signatures of strong couplings in open quantum systems and a straightforward path for numerical simulations. To validate the accuracy of the method, we apply it to two canonical models: a single spin immersed in a bosonic bath and two noninteracting spins in a common bath. In both cases, we study the transient regime and the steady state limit at nonzero temperature and spanning system-bath interactions from the weak to the strong regime. By comparing the results of the effective Hamiltonian theory with numerically exact simulations, we show that although the former overlooks non-Markovian features in the transient equilibration dynamics, it correctly captures non-perturbative bath-generated couplings between otherwise non-interacting spins, as observed in their synchronization dynamics and correlations. Altogether, the effective Hamiltonian theory offers a powerful approach for understanding strong coupling dynamics and thermodynamics, capturing the signatures of such interactions in both relaxation dynamics and in the steady state limit.

Designing optimal protocols in Bayesian quantum parameter estimation with higher-order operations

Using quantum systems as sensors or probes has been shown to greatly improve the precision of parameter estimation by exploiting unique quantum features such as entanglement. A major task in quantum sensing is to design the optimal protocol, i.e., the most precise one. It has been solved for some specific instances of the problem, but in general even numerical methods are not known. Here, we focus on the single-shot Bayesian setting, where the goal is to find the optimal initial state of the probe (which can be entangled with an auxiliary system), the optimal measurement, and the optimal estimator function. We leverage the formalism of higher-order operations to develop a method based on semidefinite programming that finds a protocol that is close to the optimal one with arbitrary precision. Crucially, our method is not restricted to any specific quantum evolution, cost function, or prior distribution, and thus can be applied to any estimation problem. Moreover, it can be applied to both single-parameter or multiparameter estimation tasks. We demonstrate our method with three examples, consisting of unitary phase estimation, thermometry in a bosonic bath, and multiparameter estimation of an SU(2) transformation. Exploiting our methods, we extend several results from the literature. For example, in the thermometry case, we find the optimal protocol at any finite time and quantify the usefulness of entanglement. Published by the American Physical Society 2024

State diagrams to determine tree tensor network operators

This work is concerned with tree tensor network operators (TTNOs) for representing quantum Hamiltonians. We first establish a mathematical framework connecting tree topologies with state diagrams. Based on these, we devise an algorithm for constructing a TTNO given a Hamiltonian. The algorithm exploits the tensor product structure of the Hamiltonian to add paths to a state diagram, while combining local operators if possible. We test the capabilities of our algorithm on random Hamiltonians for a given tree structure. Additionally, we construct explicit TTNOs for nearest neighbour interactions on a tree topology. Furthermore, we derive a bound on the bond dimension of tensor operators representing arbitrary interactions on trees. Finally, we consider an open quantum system in the form of a Heisenberg spin chain coupled to bosonic bath sites as a concrete example. We find that tree structures allow for lower bond dimensions of the Hamiltonian tensor network representation compared to a matrix product operator structure. This reduction is large enough to reduce the number of total tensor elements required as soon as the number of baths per spin reaches 3.

Bexcitonics: Quasiparticle approach to open quantum dynamics.

We develop a quasiparticle approach to capture the dynamics of open quantum systems coupled to bosonic thermal baths of arbitrary complexity based on the Hierarchical Equations of Motion (HEOM). This is done by generalizing the HEOM dynamics and mapping it into that of the system in interaction with a few bosonic fictitious quasiparticles that we call bexcitons. Bexcitons arise from a decomposition of the bath correlation function into discrete features. Specifically, bexciton creation and annihilation couple the auxiliary density matrices in the HEOM. The approach provides a systematic strategy to construct exact quantum master equations that include the system-bath coupling to all orders even for non-Markovian environments. Specifically, by introducing different metrics and representations for the bexcitons it is possible to straightforwardly generate different variants of the HEOM, demonstrating that all these variants share a common underlying quasiparticle picture. Bexcitonic properties, while unphysical, offer a coarse-grained view of the correlated system-bath dynamics and its numerical convergence. For instance, we use it to analyze the instability of the HEOM when the bath is composed of underdamped oscillators and show that it leads to the creation of highly excited bexcitons. The bexcitonic picture can also be used to develop more efficient approaches to propagate the HEOM. As an example, we use the particle-like nature of the bexcitons to introduce mode-combination of bexcitons in both number and coordinate representation that uses the multi-configuration time-dependent Hartree to efficiently propagate the HEOM dynamics.

Enhanced entanglement in multi-bath spin-boson models

The spin-boson model usually considers a spin coupled to a single bosonic bath. However, some physical situations require coupling of the spin to multiple environments. For example, spins interacting with phonons in three-dimensional magnetic materials. Here, we consider a spin coupled isotropically to three independent baths. We show that coupling to multiple baths can significantly increase entanglement between the spin and its environment at zero temperature. The effect of this is to reduce the spin's expectation values in the mean force equilibrium state. In contrast, the classical three-bath spin equilibrium state turns out to be entirely independent of the environmental coupling. These results reveal purely quantum effects that can arise from multi-bath couplings, with potential applications in a wide range of settings, such as magnetic materials.

Two-dimensional open quantum system in dissipative bosonic heat bath, external magnetic field, and two time-dependent electric fields.

Non-Markovian dynamics of a charged particle in a two-dimensional harmonic oscillator linearly coupled to a neutral bosonic heat bath is investigated in an external uniform magnetic field and two perpendicular time-dependent electric fields. The analytical expressions for the time-dependent and asymptotic angular momentum are derived for the Markovian and non-Markovian dynamics. The dependence of the angular momentum on the frequency of the electric field, cyclotron frequency, collective frequency, and anisotropy of the heat bath is studied. The angular momentum (or magnetization) of a charged particle can be ruled by varying the frequency of the electric field.

Cooling dynamics of a free ion in a Bose-Einstein condensate

We investigate the dynamics of an ion moving through a homogeneous Bose-Einstein condensate (BEC) after an initial momentum is imparted. For this, we derive a master equation in the weak-coupling limit and Lamb-Dicke approximation for the reduced density matrix of the ion. We study the time evolution of the ion's kinetic energy and observe that its expectation value, identified as the ion temperature Tion, is reduced by several orders of magnitude in a time on the order of microseconds for a condensate density in the experimentally relevant range between 1013cm−3 and 1014cm−3. We characterize this behavior by defining the duration at half maximum as the time required by Tion to reach half of its initial value, and study its dependence on the system parameters. Similarly, we find that the expectation value of the ion's momentum operator is reduced by nine orders of magnitude on the same timescale, making the ion's position converge to a final value. Based on these results, we conclude that the interaction with the bosonic bath allows for cooling and pinning of the ion by decreasing the expectation value of its kinetic energy and velocity, which constitutes a result of direct relevance for current atom-ion experiments. Published by the American Physical Society 2024

Pure Decoherence of the Jaynes–Cummings Model: Initial Entanglement with the Environment, Spin Oscillations and Detection of Non-Orthogonal States

A model based on pure decoherence for the Jaynes–Cummings spin–boson system, coupled through its integral of motion to an infinite bosonic bath, is proposed and examined. The properties of the spin oscillation process suggest an initial entanglement between the environment and the spin–boson degrees of freedom. The study demonstrates that the potential applicability of the Jaynes–Cummings model in detecting non-orthogonal bosonic states is preserved in the presence of pure decoherence.

Prethermalization in an open quantum system coupled to a spatially correlated bosonic bath

A nearly-integrable isolated quantum many-body system reaches a quasi-stationary prethermal state before a late thermalization. Here, we revisit a particular example in the settings of an open quantum system (OQS). We consider a collection of non-interacting atoms coupled to a spatially correlated bosonic bath characterized by a bath correlation length. Our result implies that the integrability of the system depends on such a correlation length. If this length is much larger than the distance between the atoms, such a system behaves as a nearly-integrable OQS. We study the properties of the emerging prethermal state for this case, i.e. the state’s lifetime, the extensive number of existing quasi-conserved quantities, the emergence of the generalized Gibbs state, and the scaling of von Neumann entropy, etc. We find that for the prethermal state, the maximum growth of entropy is logarithmic with the number of atoms, whereas such growth is linear for the final steady state, which is the Gibbs state in this case. Finally, we discuss how such prethermal states can have significant applications in quantum entanglement storage devices.

Optimal control strategies for parameter estimation of quantum systems

Optimal control theory is an effective tool to improve parameter estimation of quantum systems. Different methods can be employed for the design of the control protocol. They can be based either on Quantum Fischer Information (QFI) maximization or selective control processes. We describe the similarities, differences, and advantages of these two approaches. A detailed comparative study is presented for estimating the parameters of a spin-1/2 system coupled to a bosonic bath. We show that the control mechanisms are generally equivalent, except when the decoherence is not negligible or when the experimental setup is not adapted to the QFI. In this latter case, the precision achieved with selective controls can be several orders of magnitude better than that given by the QFI.