The decoherence of a two-state system coupled with a sub-Ohmic bath is investigated theoretically by means of the perturbation approach based on a unitary transformation. It is shown that the decoherence depends strongly and sensitively on the structure of environment. Nonadiabatic effect is treated through the introduction of a function $ξ_k$ which depends on the boson frequency and renormalized tunneling. The results are as follows:(1) the non-equilibrium correlation function $P(t)$, the dynamical susceptibility $χ''(ω)$ and the equilibrium correlation function $C(t)$ are analytically obtained for $s\leq 1$; (2) the phase diagram of thermodynamic transition shows the delocalized-localized transition point $α_l$ which agrees with exact results and numerical data from the Numerical Renormalization Group; (3) the dynamical transition point $α_c$ between coherent and incoherent phase is explicitly given for the first time. A crossover from the coherent oscillation to incoherent relaxation appears with increasing coupling (for $α> α_c $, the coherent dynamics disappear); (4) the Shiba's relation and sum rule are exactly satisfied when $α\leq α_c $; (5) an underdamping-overdamping transition point $α_c^{*}$ exists in the function $S(ω)$. Consequently, the dynamical phase diagrams in both ohmic and sub-Ohmic case are mapped out. For $Δ\ll ω_c$, the critical couplings ($α_l, α_c$ and $α_c^{*}$) are proportional to $Δ^{1-s}$.
Using the numerical path integral method we investigate the decoherence and relaxation of qubits coupled to an Ohmic bath directly and via an intermediate harmonic oscillator (IHO). Here, we suppose the oscillation frequencies of the bath modes are higher than the IHO's. When we choose suitable parameters the qubits in the two models may have almost same decoherence and relaxation times. However, the decoherence and relaxation times of the qubit in the qubit-IHO-bath model can be modulated through changing the coupling coefficients of the qubit-IHO and IHO-bath and the oscillation frequency of…
Using the numerical path integral method we investigate the decoherence and relaxation of qubits in spin-boson (SB) and spin-intermediate harmonic oscillator (IHO)-bath (SIB) models. The cases that the environment baths with low and medium frequencies are investigated. It is shown that the qubits in SB and SIB models have the same decoherence and relaxation as the baths with low frequencies. However, the qubits in the two models have different decoherence and relaxation as the baths with medium frequencies. The decoherence and relaxation of the qubit in SIB model can be modulated through chang…
In this paper, the dynamics of quantum Fisher information of a qubit interacting with a squeezed thermal environment are studied. The optimal initial state of the qubit, the temperature of the environment, and the interaction time, which maximize quantum Fisher information are obtained. Based on the ohmicity of the environment, we compare the dynamics of quantum Fisher information in ohmic, sub-ohmic, and super-ohmic regimes of the environment. Moreover, it is shown that the precise estimation of parameters is robust against squeezing.
We present a scheme to express a bath correlation function (BCF) corresponding to a given spectral density (SD) as a sum of damped harmonic oscillations. Such a representation is needed, for example, in many open quantum system approaches. To this end we introduce a class of fit functions that enables us to model ohmic as well as superohmic behavior. We show that these functions allow for an analytic calculation of the BCF using pole expansions of the temperature dependent hyperbolic cotangent. We demonstrate how to use these functions to fit spectral densities exemplarily for cases encountere…
In this paper we study the decoherence and purity of a driven solid-state qubit in the Ohmic bath by using the method based on the master equation. At first, instead of solving the master equation we investigate the coefficients of the equation which describe the shift in frequency, diffusive, decoherence, and so on. It is shown that one of the coefficients (we called it decoherence coefficient) is crucial to the decoherence of the qubit in the model. Then we investigate the evolution of the purity of the state in the model. From the analysis of the purity we see that the decoherence time of t…
The spin-boson model is studied by means of flow equations for Hamiltonians. Our truncation scheme includes all coupling terms which are linear in the bosonic operators. Starting with the canonical generator $η_c=[H_0,H]$ with $H_0$ resembling the non-interacting bosonic bath, the flow equations exhibit a universal attractor for the Hamiltonian flow. This allows to calculate equilibrium correlation functions for super-Ohmic, Ohmic and sub-Ohmic baths within a uniform framework including finite bias.
We address a particular instance where open quantum systems may be used as quantum probes for an emergent property of a complex system, as the temperature of a thermal bath. The inherent fragility of the quantum probes against decoherence is the key feature making the overall scheme very sensitive. The specific setting examined here is that of quantum thermometry, which aims to exploits decoherence as resource to estimate the temperature of a sample. We focus on temperature estimation for a bosonic bath at equilibrium in the Ohmic regime (ranging from sub-Ohmic to super- Ohmic), by using pairs…
We show that the critical exponent of a quantum phase transition in a damped-driven open system is determined by the spectral density function of the reservoir. We consider the open-system variant of the Dicke model, where the driven boson mode and also the large N-spin couple to independent reservoirs at zero temperature. The critical exponent, which is $1$ if there is no spin-bath coupling, decreases below 1 when the spin couples to a sub-Ohmic reservoir.
The spin-boson model is analytically studied using displaced Fock states (DFS) without discretization of the continuum bath. In the orthogonal displaced Fock basis, the ground-state wavefunction can be systematically improved in a controllable way. Interestingly, the zeroth-order DFS reproduces exactly the well known Silbey-Harris results. In the framework of the second-order DFS, the magnetization and the entanglement entropy are exactly calculated. It is found that the magnetic critical exponent $β$ is converged to $0.5$ in the whole sub-Ohmic bath regime $0<s<1$, compared with that by the e…
We show theoretically how the periodic coupling between an engineered reservoir and a quantum Brownian particle leads to the formation of a dynamical steady state which is characterized by an effective temperature above the temperature of the environment. The average steady state energy of the system has a higher value than expected from the environmental properties. The system experiences repeatedly a non-Markovian behavior -- as a consequence the corresponding effective decay for long evolution times is always on average stronger than the Markovian one. We also highlight the consequences of …
An approach based on a non-Markovian time-convolutionless polaron master equation is used to probe the quantum dynamics of a chromophore-qubit in a super-Ohmic bath. Utilizing a measure of non-Markovianity based on dynamical fixed points, we study the effects of the environment temperature and the coupling strength on the non-Markovian behavior of the chromophore in a super-Ohmic bath. It is found that an increase in the temperature results in a reduction in the backflow information from the environment to the chromophore, and therefore, a suppression of non-Markovianity. In the weak coupling …
By employing the spin-boson model in a dense limit of environmental modes, quantum entanglement and correlation of sub-Ohmic and Ohmic baths for dissipative quantum phase transitions are numerically investigated based on the variational principle. With several measures borrowed from quantum information theory, three different types of singularities are found for the first-order, second-order, and Kosterlitz-Thouless phase transitions, respectively, and the values of transition points and critical exponents are accurately determined. Besides, the scaling form of the quantum discord in the Ohmic…
We consider an $S=1/2$ antiferromagnetic quantum Heisenberg chain where each site is coupled to an independent bosonic bath with ohmic dissipation. The coupling to the bath preserves the global SO(3) spin symmetry. Using large-scale, approximation-free quantum Monte Carlo simulations, we show that any finite coupling to the bath suffices to stabilize long-range antiferromagnetic order. This is in stark contrast to the isolated Heisenberg chain where spontaneous breaking of the SO(3) symmetry is forbidden by the Mermin-Wagner theorem. A linear spin-wave theory analysis confirms that the memory …
The evolution of a quantum system towards thermal equilibrium is usually studied by approximate methods, which have their limits of validity and should be checked against analytically solvable models. In this paper, we propose an analytically solvable model to investigate the energy transfer between a bosonic bath and a fermionic chain which are nonlinearly-coupled to each other. The bosonic bath consists of an infinite collection of non-interacting bosonic modes, while the fermionic chain is represented by a chain of interacting fermions with nearest-neighbor interactions. We compare behavior…
The Dirac-Frenkel time-dependent variation is employed to probe the dynamics of the zero temperature sub-Ohmic spin-boson model with strong friction utilizing the Davydov D1 ansatz. It is shown that initial conditions of the phonon bath have considerable influence on the dynamics. Counterintuitively, even in the very strong coupling regime, quantum coherence features still manage to survive under the polarized bath initial condition, while such features are absent under the factorized bath initial condition. In addition, a coherent-incoherent transition is found at a critical coupling strength…
The quantum average energy decay and the purity decay are studied for a system particle as a function of the number of constituents of a discrete bath model. The system particle is subjected to two distinct physical situations: the harmonic oscillator (HO) and the Morse potential. The environment (bath) is composed by a {\it finite} number N of uncoupled HOs, characterizing the structured bath, which in the limit $N\to\infty$ is assumed to have an ohmic, sub-ohmic or super-ohmic spectral density. For very low values of N the mean energy and purity remain constant in time but starts to decay fo…
We address the discrimination of structured baths at different temperatures by dephasing quantum probes. We derive the exact reduced dynamics and evaluate the minimum error probability achievable by three different kinds of quantum probes, namely a qubit, a qutrit and a quantum register made of two qubits. Our results indicate that dephasing quantum probes are useful in discriminating low values of temperature, and that lower probabilities of error are achieved for intermediate values of the interaction time. A qutrit probe outperforms a qubit one in the discrimination task, whereas a register…
We study how to control the dynamics of tripartite entanglement among optical cavities using non-Markovian baths. In particular, we demonstrate how the reservoir engineering through the utilization of non-Markovian baths with different types of Lorentzian and ohmic spectral densities can lead to an entanglement survival for longer times and in some cases considerable regain of seemingly lost entanglement. Both of these behaviors indicate a better sustainability of entanglement (in time) compared to the usual Markovian bath situations which assumes a flat spectrum of the bath around the system …
We investigate a spin-boson model with two boson baths that are coupled to two perpendicular components of the spin by employing the density matrix renormalization group method with an optimized boson basis. It is revealed that in the deep sub-Ohmic regime there exists a novel second-order phase transition between two types of doubly degenerate states, which is reduced to one of the usual type for nonzero tunneling. In addition, it is found that expectation values of the spin components display jumps at the phase boundary in the absence of bias and tunneling.
Developed originally for the Holstein polaron, the Davydov D1 ansatz is an efficient, yet extremely accurate trial state for time-dependent variation of the spin-boson model [J. Chem. Phys. 138, 084111 (2013)]. In this work, the Dirac-Frenkel time-dependent variational procedure utilizing the Davydov D1 ansatz is implemented to study entanglement dynamics of two qubits under the influence of two independent baths. The Ohmic spectral density is used without the Born-Markov approximation or the rotating-wave approximation. In the strong coupling regime finite-time disentanglement is always found…
We study the dynamics of a quantum two state system driven through an avoided crossing under the influence of a super Ohmic environment, i.e. a longitudinal as well as a transversal one. The crossing time window, in which relaxation influences the dynamics, is centered around the avoided crossing. We determine the dynamics and the Landau-Zener probability employing the numerical exact quasi-adiabatic path integral. At weak coupling we show that the numerically less demanding nonequilibrium Bloch equations provide an accurate description. The crossing time depends strongly not only on the syste…
With a decomposition scheme for the bath correlation function, the hierarchical equations of motion (HEOM) are extended to the zero-temperature sub-Ohmic and Ohmic spin-boson model. We investigate the linear absorption spectrum of the sub-Ohmic and Ohmic spin-boson model at zero temperature. By applying the extended HEOM, the equilibrium spin dynamics are obtained approximately. Then the linear response function is calculated according to the Kubo formula rewritten in Liouville space. To explore the essence of phase transition, we compute the linear absorption spectrum defined by the linear re…
By means of a trial wave function, the multi-D$_1$ ansatz, extensive variational calculations with more than ten thousand parameters have been carried out to study quantum phase transitions in the ground states of a two-impurity system embedded in a common Ohmic bath of bosons. Quantum criticality in both the impurity system and the Ohmic bosonic bath is investigated with relevant transition points and critical exponents determined accurately. With the linear grid of the Ohmic spectral density, our numerical calculations produce a much better description of the ground states with lower energie…
In the long-time limit, an open quantum system coupled to a dissipative environment is believed to lose its coherence without driving or measurement. Counterintuitively, we provide a necessary condition on trapping the coherence of a two-level system entirely with a thermal bath. Based on a time-local master equation, it is found that the residue coherence survives even under a high-temperature bath as long as the long-time Lamb shift is exactly negative to the system transition frequency. This condition is generally met in the strong and even ultrastrong coupling regime that could be relaxed …
Quantum probing consists of suitably exploiting a simple, small, and controllable quantum system to characterize a larger and more complex system. Here, we address the estimation of the cutoff frequency of the Ohmic spectral density of a harmonic reservoir by quantum probes. To this aim, we address the use of single-qubit and two-qubit systems and different kinds of coupling with the bath of oscillators. We assess the estimation precision by the quantum Fisher information of the sole quantum probe as well as the corresponding quantum signal-to-noise ratio. We prove that, for most of the values…
The von Neumann entropy of various quantum dissipative models is calculated in order to discuss the entanglement properties of these systems. First, integrable quantum dissipative models are discussed, i.e., the quantum Brownian motion and the quantum harmonic oscillator. In case of the free particle, the related entanglement of formation shows no non-analyticity. In case of the dissipative harmonic oscillator, there is a non-analyticity at the transition of underdamped to overdamped oscillations. We argue that this might be a general property of dissipative systems. We show that similar featu…
We study the bath correlation functions (BCFs) of open quantum systems interacting with thermal baths, in case the spectral densities (SDs) exhibit removable logarithmic singularities at low frequencies and are arbitrarily shaped at higher frequencies. The singularities consist in arbitrarily positive or negative powers of logarithmic functions, as additional factors for the power laws of the Ohmic-like SDs. If the SD vanishes sufficiently fast at high frequencies the short time behavior of the BCF is algebraic. The long time behavior of the BCF exhibits a variety of relaxations that involve i…
We report an anomalous decoherence phenomenon of a quantum dissipative system in the framework of a stochastic decoupling scheme along with a hierarchical equations-of-motion formalism without the usual Born-Markov or weak coupling approximations. It is found that the decoherence of a two-qubit spin-boson model can be reduced by increasing the bath temperature in strong-coupling regimes. For the weak-coupling situation, we find that the bath temperature may enhance the decoherence. This result is contrary to the common recognition that a higher bath temperature always induces a more severe dec…
We use a non-Markovian approach to study the decoherence dynamics of a qubit in either a low- or high-frequency bath modeling the qubit environment. This approach is based on a unitary transformation and does not require the rotating-wave approximation. We show that for low-frequency noise, the bath shifts the qubit energy towards higher energies (blue shift), while the ordinary high-frequency cutoff Ohmic bath shifts the qubit energy towards lower energies (red shift). In order to preserve the coherence of the qubit, we also investigate the quantum Zeno effect in two cases: low- and high-freq…
Study of dissipative quantum phase transitions in the Ohmic spin-boson model is numerically challenging in a dense limit of environmental modes. In this work, large-scale numerical simulations are carried out based on the variational principle. The validity of variational calculations, spontaneous breakdown of symmetries, and quantum fluctuations and correlations in the Ohmic bath are carefully analyzed, and the critical coupling as well as exponents are accurately determined in the weak tunneling and continuum limits. In addition, quantum criticality of the Ohmic bath is uncovered both in the…
In this work, the exact dynamics of excitation in the generalized Aubry-André-Harper model coupled with an Ohmic-type environment is discussed by evaluating the survival probability and inverse participation ratio of the state of system. In contrast to the common belief that localization will preserve the information of the initial state in the system against dissipation into the environment, our study found that strong localization can enhance the dissipation of quantum information instead. By a thorough examination of the dynamics, we show that the coherent transition between the energy stat…
The dissipative quantum dynamics of an anharmonic oscillator coupled to a bath is studied with the purpose of elucidating the differences between the relaxation to a spin bath and to a harmonic bath. Converged results are obtained for the spin bath by the Surrogate Hamiltonian approach. This method is based on constructing a system-bath Hamiltonian, with a finite but large number of spin bath modes, that mimics exactly a bath with an infinite number of modes for a finite time interval. Convergence with respect to the number of simultaneous excitations of bath modes can be checked. The results …
We study a class of quantum measurement models. A microscopic object is entangled with a macroscopic pointer such that each eigenvalue of the measured object observable is tied up with a specific pointer deflection. Different pointer positions mutually decohere under the influence of a bath. Object-pointer entanglement and decoherence of distinct pointer readouts proceed simultaneously. Mixtures of macroscopically distinct object-pointer states may then arise without intervening macroscopic superpositions. Initially, object and apparatus are statistically independent while the latter has point…
The entanglement dynamics in a bipartite system consisting of a qubit and a harmonic oscillator interacting only through their coupling with the same bath is studied. The considered model assumes that the qubit is coupled to the bath via the Jaynes-Cummings interaction, whilst the position of the oscillator is coupled to the position of the bath via a dipole interaction. We give a microscopic derivation of the Gorini-Kossakowski-Sudarshan-Lindblad equation for the considered model. Based on the Kossakowski Matrix, we show that non-classical correlations including entanglement can be generated …
An analytic ground state is proposed for the unbiased spin-boson Hamiltonian, which is non-Gaussian and beyond the Silbey-Harris ground state with lower ground state energy. The infrared catastrophe in Ohmic and sub-Ohmic bosonic bath plays an important role in determining the degeneracy of the ground state. We show that the infrared divergence associated with the displacement of the nonadiabatic modes in bath may be removed from the proposed ground state for the coupling $α<α_c$. Then $α_c$ is the quantum critical point of a transition from non-degenerate to degenerate ground state and our ca…
The temperature of an oscillator coupled to the vacuum state of a heat bath via ohmic coupling is non-zero, as measured by the reduced density matrix of the oscillator. This paper shows that the actual temperature, as measured by a thermometer is still zero (or in the thermal state of the bath, the temperature of the bath). The decoherence temperature is due to "false-decoherence", with the heat bath state being dragged along with the oscillator.
We consider a qubit coupled to a nonlinear quantum oscillator, the latter coupled to an Ohmic bath, and investigate the qubit dynamics. This composed system can be mapped onto that of a qubit coupled to an effective bath. An approximate mapping procedure to determine the spectral density of the effective bath is given. Specifically, within a linear response approximation the effective spectral density is given by the knowledge of the linear susceptibility of the nonlinear quantum oscillator. To determine the actual form of the susceptibility, we consider its periodically driven counterpart, th…
A model for a quantum register dissipatively coupled with a bosonic thermal bath is studied. The register consists of $N$ qubits (i.e. spin ${1/2}$ degrees of freedom), the bath is described by $N_b$ bosonic modes. The register-bath coupling is chosen in such a way that the total number of excitations is conserved. The Hilbert space splits allowing the study of the dynamics separately in each sector. Assuming that the coupling with the bath is the same for all qubits, the excitation sectors have a further decomposition according the irreducible representations of the $su(2)$ spin algebra. The …
We study the suppression of qubit dephasing through Uhrig dynamical decoupling (UDD) in nontrivial environments modeled within the spin-boson formalism. In particular, we address the case of (i) a qubit coupled to a bosonic bath with power-law spectral density, and (ii) a qubit coupled to a single harmonic oscillator that dissipates energy into a bosonic bath, which embodies an example of a structured bath for the qubit. We then model the influence of random time jitter in the UDD protocol by sorting pulse-application times from Gaussian distributions centered at appropriate values dictated by…
The standard approach for path integral Monte Carlo simulations of open quantum systems is extended as an efficient tool to monitor the time evolution of coherences (off-diagonal elements of the reduced density matrix) also for strong coupling to environments. Specific simulations are performed for two level systems embedded in Ohmic and sub-Ohmic reservoirs in the domains of coherent and incoherent dynamics of the polarization. In the latter regime, the notorious difficulty to access the long time regime is overcome by combining simulations on moderate time scales with iteratively calculated …
The free energy of a quantum oscillator in an arbitrary heat bath at a temperature T is given by a "remarkable formula" which involves only a single integral. This leads to a corresponding simple result for the entropy. The low temperature limit is examined in detail and we obtain explicit results both for the case of an Ohmic heat bath and a radiation heat bath. More general heat bath models are also examined. This enables us to determine the entropy at zero temperature in order to check the third law of thermodynamics in the quantum regime
The deep sub-Ohmic spin-boson model shows a longstanding non-Markovian coherence at low temperature. Motivating to quench this robust coherence, the thermal effect is unitarily incorporated into the time evolution of the model, which is calculated by the adaptive time-dependent density matrix renormalization group algorithm combined with the orthogonal polynomials theory. Via introducing a unitary heating operator to the bosonic bath, the bath is heated up so that a majority portion of the bosonic excited states is occupied. It is found in this situation the coherence of the spin is quickly qu…
A novel method is introduced in order to treat the dissipative dynamics of quantum systems interacting with a bath of classical degrees of freedom. The method is based upon an extension of the Nosè-Hoover chain (constant temperature) dynamics to quantum-classical systems. Both adiabatic and nonadiabatic numerical calculations on the relaxation dynamics of the spin-boson model show that the quantum-classical Nosè-Hoover chain dynamics represents the thermal noise of the bath in an accurate and simple way. Numerical comparisons, both with the constant energy calculation and with the quantum-clas…
A Rabi dimer is used to model a recently reported circuit quantum electrodynamics system composed of two coupled transmission-line resonators with each coupled to one qubit. In this study, a phonon bath is adopted to mimic the multimode micromechanical resonators and is coupled to the qubits in the Rabi dimer. The dynamical behavior of the composite system is studied by the Dirac-Frenkel time-dependent variational principle combined with the multiple Davydov D$_{2}$ ansätze. Initially all the photons are pumped into the left resonator, and the two qubits are in the down state coupled with the …
Optimal state transfer of a single two-level system (TLS) coupled to an Ohmic boson bath via off-diagonal TLS-bath coupling is studied by using optimal control theory. In the weak system-bath coupling regime where the time-dependent Bloch-Redfield formalism is applicable, we obtain the Bloch equation to probe the evolution of the dissipative TLS in the presence of a time-dependent external control field. By using the automatic differentiation technique to compute the gradient for the cost functional, we calculate the optimal transfer integral profile that can achieve an ideal transfer within a…
We investigate the optimal control problem for non-Markovian open, dissipative quantum system. Optimal control using Pontryagin maximum principle is specifically derived. The influences of Ohmic reservoir with Lorentz-Drude regularization are numerically studied in a two-level system under the following three conditions: ω_0\llω_c, ω_0\approxω_c or ω_0\ggω_c, where ω_0 is the characteristic frequency of the quantum system of interest, and ω_c the cut-off frequency of Ohmic reservoir. The optimal control process shows its remarkable influences on the decoherence dynamics. The temperature is a k…
We propose a scheme for the quantum simulation of sub-Ohmic spin--boson models by color centers in free-standing hexagonal boron nitride (h-BN) membranes. The electronic spin of a color center that couples to the membrane vibrational spectrum constitute the physical model. The spin-motion coupling is provided by an external magnetic field gradient. In this study, we show that a class of spectral densities can be attained by engineering geometry and boundary conditions of the h-BN resonator. We then put our focus on two extreme cases, i.e. $1/f$- and white-noise spectral densities. Spin coheren…
