Controlling decoherence via PT-symmetric non-Hermitian open quantum systems

We have studied the effect of a non-Hermitian Bosonic bath on the dynamics of a two-level spin system. The non-Hermitian Hamiltonian of the bath is chosen such that it converges to the harmonic oscillator Hamiltonian when the non-Hermiticity is switched off. We calculate the dynamics of the spin system and found that the non-Hermiticity can have positive as well as negative effects on the coherence of the system. However, the decoherence can be completely eliminated by choosing the non-Hermiticity parameter and the phase of the system bath interaction appropriately. We have also studied the effect of this bath on the entanglement of a two-spin system when the bath is acting only on one spin.     

Biorthogonal quantum criticality in non-Hermitian many-body systems

We develop the perturbation theory of the fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues. The quantum criticality in the non-Hermitian transverse field Ising chain is investigated by the second derivative of the ground-state energy and the ground-state fidelity susceptibility. We show that the system undergoes a second-order phase transition with the Ising universal class by numerically computing the critical points and the critical exponents from the finite-size scaling theory. Interestingly, our results indicate that the biorthogonal quantum phase transitions are described by the biorthogonal fidelity susceptibility instead of the conventional fidelity susceptibility.     

Application of non-Hermitian Hamiltonian model in open quantum optical systems

Non-Hermitian systems have observed numerous novel phenomena and might lead to various applications. Unlike standard quantum physics, the conservation of energy guaranteed by the closed system is broken in the non-Hermitian system, and the energy can be exchanged between the system and the environment. Here we present a scheme for simulating the dissipative phase transition with an open quantum optical system. The competition between the coherent interaction and dissipation leads to the second-order phase transition. Furthermore, the quantum correlation in terms of squeezing is studied around the critical point. Our work may provide a new route to explore the non-Hermitian quantum physics with feasible techniques in experiments.     

Open quantum systems with time-dependent Hamiltonians and their linear response

We give a rigorous (Hamiltonian) treatment of a quantum system weakly coupled to an infinite free reservoir and subject to an external time-dependent driving potential varying on the scale of dissipation. The linear response of the system initially in thermal equilibrium is determined and compared with the usual expressions of linear response theory.Work partly supported by NSF grant no. MPS 75-11864-A04.On leave of absence from Fachbereich Physik der Universität München. Work supported by a DFG fellowship.     

Maximally robust unravelings of quantum master equations

The stationary state of an open quantum system has infinitely many representations as an ensemble of pure states. We argue that the most natural ensemble is the most robust physically realizable ensemble. Robustness is quantified by the survival probability. Physical realization requires monitoring the environment to “unravel” the dissipative evolution.     

Remarks on pseudo-Hermitian matrices and their exceptional points

We highlight some features of pseudo-Hermitian matrices admitting exceptional points. Starting from these general considerations we discuss a fermionic time-reversal violating pseudo-Hermitian Hamiltonian which breaks diagonalizability for some critical parameter values. Partially supported by PRIN “Sintesi”. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

Quantum phase distribution and the number—phase Wigner function of the generalized squeezed vacuum states associated with solvable quantum systems

The quantum phase properties of the generalized squeezed vacuum states associated with solvable quantum systems are studied by using the Pegg-Barnett formalism.Then,two nonclassical features,i.e.,squeezing in the number and phase operators,as well as the number-phase Wigner function of the generalized squeezed states are investigated.Due to some actual physical situations,the present approach is applied to two classes of generalized squeezed states:solvable quantum systems with discrete spectra and nonlinear squeezed states with particular nonlinear functions.Finally,the time evolution of the nonclassical properties of the considered systems has been numerically investigated.     

Measure of irreversibility and entropy production in open quantum systems

A new concept of a measure of irreversibility for quantum dynamics in open systems is introduced as a suitably regularized substitute for the common notion of entropy production, which, unfortunately, yields infinite values for so many irreversible processes of physical relevance.     

On the standard quantum Brownian equation and an associated class of non-autonomous master equations

It is shown that the standard quantum Brownian equation (QBE) can violate positivity not only past the thermal correlation time, but at arbitrarily long times at high system frequencies. In an effort to improve the standard QBE, exact operator solutions are provided for a class of non-autonomous master equations. These exact solutions are used to derive sufficient positivity conditions for the coefficients of the master equations.     

A fluctuation theorem for Floquet quantum master equations

We present a fluctuation theorem for Floquet quantum master equations. This is a detailed version of the famous Gallavotti–Cohen theorem. In contrast to the latter theorem, which involves the probability distribution of the total heat current, the former involves the joint probability distribution of positive and negative heat currents and can be used to derive the latter. A quantum two-level system driven by a periodic external field is used to verify this result.     

Simplerealizations of generalized measurements in quantum mechanics

This paper discusses the approach to the analysis of measurements in quantum mechanics which is based on a set of "detection operators" forming a resolution of identity. The expectation value of each of these operators furnishes the counting rate at a detector for any object state that is prepared. "Predictable measurements" are those for which there is a representation in which only one element of each diagonal matrix representing each operator is not zero. A set of commuting detection operators defines the class of "spectral measurements", which may be either predictable or not. An even more general definition of measurement may be given by abandoning the requirement of commutativity of the detection operators. In this case one cannot define an observable which corresponds to a single self-adjoint operator, which violates the standard theory of quantum mechanical measurement. Simple experimental realizations of each of these classes of measurement are suggested.     

Influences of spin–orbit interaction on quantum speed limit and entanglement of spin qubits in coupled quantum dots

Quantum speed limit and entanglement of a two-spin Heisenberg XYZ system in an inhomogeneous external magnetic field are investigated. The physical system studied is the excess electron spin in two adjacent quantum dots. The influences of magnetic field inhomogeneity as well as spin–orbit coupling are studied. Moreover, the spin interaction with surrounding magnetic environment is investigated as a non-Markovian process. The spin–orbit interaction provides two important features: the formation of entanglement when two qubits are initially in a separated state and the degradation and rebirth of the entanglement.     

Number-resolved master equation approach to quantum measurement and quantum transport

In addition to the well-known Landauer–Büttiker scattering theory and the nonequilibrium Green’s function technique for mesoscopic transports, an alternative (and very useful) scheme is quantum master equation approach. In this article, we review the particle-number (n)-resolved master equation (n-ME) approach and its systematic applications in quantum measurement and quantum transport problems. The n-ME contains rich dynamical information, allowing efficient study of topics such as shot noise and full counting statistics analysis. Moreover, we also review a newly developed master equation approach (and its n-resolved version) under self-consistent Born approximation. The application potential of this new approach is critically examined via its ability to recover the exact results for noninteracting systems under arbitrary voltage and in presence of strong quantum interference, and the challenging non-equilibrium Kondo effect.     

Exact time evolution and second-order quantum master equations for two interacting qubits

Time evolution of two interacting qubits under the influence of thermal reservoirs is considered. When there is only one excitation in the whole system, an exact reduced dynamics can be obtained. The result is compared with those obtained by the time-convolutionless and time-convolution quantum master equations in the second order approximation.     

Evaluation of dynamical properties of open quantum systems using the driven Liouville-von Neumann approach: methodological considerations

Methodological aspects of using the driven Liouville-von Neumann (DLvN) approach for simulating dynamical properties of molecular junctions are discussed. As a model system we consider a non-interacting resonant level uniformly coupled to a single Fermionic bath. We demonstrate how a finite system can mimic the depopulation dynamics of the dot into an infinite band bath of continuous and uniform density of states. We further show how the effects of spurious energy resolved currents, appearing due to the approximate nature of the equilibrium state obtained in DLvN calculations, can be avoided. Several ways to approach the wide band limit, which is often adopted in analytical treatments, using a finite numerical model system are discussed including brute-force increase of the lead model bandwidth as well as efficient cancellation or direct subtraction of finite-bandwidth effect. These methodological considerations may be relevant also for other numerical schemes that aim to study non-equilibrium thermodynamics via simulations of open quantum systems.     

A note on the asymptotic master equations for systems with bound states

It is shown that, within the convolutionless formalism of Fuliski, the asymptotic form (in time) of the Liouville equation does not change with the existence of bound states in the energy spectrum of the system under consideration.     

Time evolution and spectral concentration in quantum systems

Time dependence and spectral concentration in quantum systems are reviewed. A partitioning technique is presented based on retarded and advanced propagators. The associated fundamental time symmetry is conveniently formulated in correspondence with the classical notion of reversal of time and momenta. Symmetry breakings occur when a particular convolution product is broken up into past and future times.The separation of the time variable into two scales is discussed. Comparison with the wave and reaction operator formulation gives a reciprocal relationship between these times together with an emphasis of the role played by the associated spectral density. Examples are given from applications of Weyl's complex eigenvalue theory.