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 the qubit decrease with the increase of the amplitude of the driven fields and it is increase with the increase of the frequency of the driven fields.
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…
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.
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 obtain…
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…
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…
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…
We explore a dynamic signature of quantum phase transition (QPT) in an isotropic Lipkin-Meshkov-Glick (LMG) model by studying the time evolution of a central qubit coupled to it. We evaluate exactly the time-dependent purity, which can be used to measure quantum coherence, of the central qubit. It is found that distinctly different behaviors of the purity as a function of the parameter reveal clearly the QPT point in the system. It is also clarified that the present model is equivalent to an anti Jaynes-Cummings model under certain conditions.
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…
We present a systematic study of the purity for Gaussian states of single-mode continuous variable systems. We prove the connection of purity to observable quantities for these states, and show that the joint measurement of two conjugate quadratures is necessary and sufficient to determine the purity at any time. The statistical reliability and the range of applicability of the proposed measurement scheme is tested by means of Monte Carlo simulated experiments. We then consider the dynamics of purity in noisy channels. We derive an evolution equation for the purity of general Gaussian states b…
We investigate the influence of AC driving fields on the coherence properties of one- and two-qubit gate operations. In both cases, we find that for suitable driving parameters, the gate purity improves significantly. A mapping of the time-dependent system-bath model to an effective static model provides analytical results. The resulting purity loss compares favorably with numerical results.
The purity of quantum states is a key requirement for many quantum applications. Improving the purity is limited by fundamental laws of thermodynamics. Here we are probing the fundamental limits for a natural approach to this problem, namely heat-bath algorithmic cooling(HBAC). The existence of the cooling limit for HBAC techniques was proved by Schulman et al. in, the limit however remained unknown for the past decade. Here for the first time we find this limit. In the context of quantum thermodynamics, this corresponds to the maximum extractable work from the quantum system.
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 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 …
We study the non-Markovian dynamics of a qubit made up of a two-level atom interacting with an electromagnetic field (EMF) initially at finite temperature. Unlike most earlier studies where the bath is assumed to be fixed, we study the coherent evolution of the combined qubit-EMF system, thus allowing for the back-action from the bath on the qubit and the qubit on the bath in a self-consistent manner. In this way we can see the development of quantum correlations and entanglement between the system and its environment, and how that affects the decoherence and relaxation of the system. We find …
We derive a quantum Langevin equation for a quantum spin in the presence of a magnetic field and study its dynamics in the Markovian limit using the Ohmic bath model. We extend our analysis to the Drude bath with a finite memory. We study the time evolution of the expectation values of the magnetic moments. The spin auto-correlation functions exhibit a damped oscillatory behaviour with the randomization time being determined by the damping rate and also the memory time for the Drude bath model. We also analyse the spin response function of the system for the Ohmic bath model. Our results are c…
This article has to do with the derivation and solution of the Fokker--Planck equation associated to the momentum-independent Wigner function, of a particle subjected to a harmonic external field and immersed in a ohmic thermal bath of quantum harmonic oscillators. The strategy employed is a simplified version of the phenomenological approach of Schramm, Jung and Grabert of interpreting the operators as c-numbers to derive the adjoint equation arising from a twofold transformation of the Wigner function of the entire phase space. The statistical properties of the random noise comes from the in…
We obtain an upper bound on the time available for quantum computation for a given quantum computer and decohering environment with quantum error correction implemented. First, we derive an explicit quantum evolution operator for the logical qubits and show that it has the same form as that for the physical qubits but with a reduced coupling strength to the environment. Using this evolution operator, we find the trace distance between the real and ideal states of the logical qubits in two cases. For a super-Ohmic bath, the trace distance saturates, while for Ohmic or sub-Ohmic baths, there is …
The dynamics of two coupled spins-1/2 interacting with a spin-bath via the quantum Heisenberg XY coupling is studied. The pair of central spins served as a quantum open subsystem are initially prepared in two types of states: the product states and the Bell states. The bath, which consists of $N$ (in the thermodynamic limit $N\to\infty$) mutually coupled spins-1/2, is in a thermal state at the beginning. By the Holstein-Primakoff transformation, the model can be treated effectively as two spin qubits embedded in a single mode cavity. The time-evolution of the purity, z-component summation and …
Numerical and analytic results have been used to characterize quantum transport in spin chains, showing the existence of both ballistic and diffusive motion. Experiments have shown that heat transfer is surprisingly always diffusive. The scattering from phonons and impurities have been postulated to be the two factors critical in causing the diffusive transport. In this work, we evaluate the transport process by incorporating a bath of phonons and impurities in order to understand the role played by each of the factors. While methods like time-dependent density matrix renormalization group (tD…
By using the Redfield form of the master equation, we investigate the decoherence times of a double quantum dot charge qubit (DQDCQ) in three different cases, namely when it is coupled to (I) the piezoelectric coupling phonon bath (PCPB), (II) the deformation coupling phonon bath (DCPB), and (III) the Ohmic bath. It is found that our results for case (I) and (II) are in the same magnitude with those obtained via the exact path integral methods, while for case (III), the decoherence time is in well agreement with the experimental value.
For the generalized master equations derived by Karrlein and Grabert for the microscopic model of a damped harmonic oscillator, the conditions for purity of states are written, in particular for different initial conditions and different types of damping, including Ohmic, Drude and weak coupling cases, Agarwal and Weidlich-Haake models. It is shown that the states which remain pure are the squeezed states with constant in time variances. For pure states, the generalized nonlinear Schr\" odinger-type equations corresponding to these master equations are also obtained. Then the condition for pur…
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…
We investigate the use of continuously-applied external fields to maximize the fidelity of quantum logic operations performed on a decohering qubit. Assuming a known error operator and an environment represented by a scalar boson field at a finite temperature, we show how decoherence during logical operations can be efficiently reduced by applying a superposition of two external vector fields: one rotating orthogonally to the direction of the other, which remains static. The required field directions, frequency of rotation and amplitudes to decouple noise dynamically are determined by the coup…
We explore the spin-boson model in a special case, i.e., with zero local field. In contrast to previous studies, we find no possibility for quantum phase transition (QPT) happening between the localized and delocalized phases, and the behavior of the model can be fully characterized by the even or odd parity as well as the parity breaking, instead of the QPT, owned by the ground state of the system. Our analytical treatment about the eigensolution of the ground state of the model presents for the first time a rigorous proof of no-degeneracy for the ground state of the model, which is independe…
Non-Markovian dynamics of two interacting two-level qubits coupled to a bosonic bath was previously studied using the quantum-state-diffusion (QSD) equation, where a stochastic state is used to describe the system. In this study, we provide another perspective on this system by deriving the analytic form of the master equation, which describes the system with a reduced density matrix. Then, we validate the master equation by examining entanglement generation and state purity. In addition, with the master equation, we observe the effects from first-order noise and notice that a good asymptotic …
We analyze an entangling protocol to generate tripartite Greenberger-Horne-Zeilinger states in a system consisting of three superconducting qubits with pairwise coupling. The dynamics of the open quantum system is investigated by taking into account the interaction of each qubit with an independent bosonic bath with an ohmic spectral structure. To this end a microscopic master equation is constructed and exactly solved. We find that the protocol here discussed is stable against decoherence and dissipation due to the presence of the external baths.
We consider a surface code suffering decoherence due to coupling to a bath of bosonic modes at finite temperature and study the time available before the unavoidable breakdown of error correction occurs as a function of coupling and bath parameters. We derive an exact expression for the error rate on each individual qubit of the code, taking spatial and temporal correlations between the errors into account. We investigate numerically how different kinds of spatial correlations between errors in the surface code affect its threshold error rate. This allows us to derive the maximal duration of e…
For quantum annealing, as opposed to circuit based quantum computing, the solution to a computational problem is encoded in the ground state of a quantum system. Therefore its susceptibility to environmental effects is a different but not less important open question essential to a scalable implementation. In this work we use renormalization group techniques to study the effect of Ohmic baths in a regime typical for practical adiabatic quantum computation. We show qualitative change to the effective Hamiltonian as well as the reduced qubit density matrix encoding entanglement between system an…
