We study the influence of an external driving field on the coherence properties of a qubit subject to bit-flip noise. In the presence of driving, two paradigmatic cases are considered: (i) a field that results for a suitable choice of the parameters in so-called coherent destruction of tunneling and (ii) one that commutes with the static qubit Hamiltonian. In each case, we give for high-frequency driving a lower bound for the coherence time. This reveals the conditions under which the external fields can be used for coherence stabilization.

We study the influence of the preparation of an open quantum system on its reduced time evolution. In contrast to the frequently considered case of an initial preparation where the total density matrix factorizes into a product of a system density matrix and a bath density matrix the time evolution generally is no longer governed by a linear map nor is this map affine. Put differently, the evolution is truly nonlinear and cannot be cast into the form of a linear map plus a term that is independent of the initial density matrix of the open quantum system. As a consequence, the inhomogeneity that emerges in formally exact generalized master equations is in fact a nonlinear term that vanishes for a factorizing initial state. The general results are elucidated with the example of two interacting spins prepared at thermal equilibrium with one spin subjected to an external field. The second spin represents the environment. The field allows the preparation of mixed density matrices of the first spin that can be represented as a convex combination of two limiting pure states, i.e. the preparable reduced density matrices make up a convex set. Moreover, the map from these reduced density matrices onto the corresponding density matrices of the total system is affine only for vanishing coupling between the spins. In general, the set of the accessible total density matrices is nonconvex.

We consider a CNOT gate operation under the influence of quantum bit-flip noise and demonstrate that ac fields can change bit-flip noise into phase noise and thereby improve coherence up to several orders of magnitude while the gate operation time remains unchanged. Within a high-frequency approximation, both purity and fidelity of the gate operation are studied analytically. The numerical treatment with a Bloch-Redfield master equation confirms the analytical results.PACS numbers: 03.67. Pp, 42.50.Hz, 03.65.Yz Despite the remarkable experimental realization of qubits [1,2,3] and two-qubit gates [4] in condensed matter systems, the construction of a working quantum computer remains an elusive goal, not only due to deficiencies of the control circuitry, but also due to the unavoidable coupling to the environment. Several proposals to overcome the ensuing decoherence have been put forward, such as the use of decoherence free subspaces [5,6,7,8,9], quantum Zeno subspaces [10], dynamical decoupling [11,12,13,14], and coherent destruction of tunneling [15].A single qubit under the influence of bit-flip noise can be modeled by the spin-boson Hamiltonianwhere σ x,z denotes Pauli matrices and ξ is a shorthand notation for the quantum noise specified below. The influence of the bath is governed by the spectral density of the noise at the tunneling frequency ∆/ . A possible driving field may couple to any projection n of the (pseudo) spin operator σ, i.e., be proportional to n · σ. In Ref.[15], two particular choices have been studied and compared against each other: A driving of the form H(t) = Aσ z cos(Ωt) commutes with the static qubit Hamiltonian while it modifies the bath coupling σx ξ in such a way that the spectral density of the bath at multiples of the driving frequency becomes relevant. For a proper driving amplitude, this eliminates noise with frequencies below the driving frequency which, thus, should lie above the cutoff frequency of the bath. This scheme represents a continuous-wave version of dynamical decoupling [15]. By contrast, a driving of the type H(t) = Aσ x cos(Ωt) renders the qubit-bath coupling unchanged but renormalizes the tunnel splitting ∆ towards smaller values and thereby causes the so-called coherent destruction of tunneling (CDT) [16,17]. Then, decoherence is determined by the spectral density of the bath at a lower effective tunnel frequency. For an ohmic bath being linear in the frequency, the consequence is that both decoherence and the coherent oscillations in the rotating frame are slowed down by the same factor [15]. Therefore, the number of coherent oscillations is not enlarged and, thus, for single-qubit operations, CDT might be of limited use.In this work, we propose a coherence stabilization scheme for a CNOT gate based on isotropic Heisenberg interaction [18,19]. Our scheme does not suffer from the drawbacks mentioned above because (i) it involves only intermediately large driving frequencies that can lie well below the bath cutoff and (ii) it does not increase the operation ...

In Ramsey atomic interferometry, a superposition of atomic states is produced by a mechanism completely equivalent (for experimental purposes) to interaction with a classical field. Since this property holds, in the case of Rydberg atoms, for temperatures close to absolute zero and field intensities of the order of a single photon, the question arises as to why the quantum nature of the field can be neglected. We model the passage of an atom through a Ramsey zone and show that, in order to explain the phenomenon, correlation properties between three subsystems and strong cavity dissipation turn out to be the essential physical ingredients leading to classical behavior. [S0031-9007(99)09302-3] PACS numbers: 39.20. + q, 42.50.Lc Microwave cavities are extensively used in experiments designed to access fundamental issues concerning the interaction of atoms and electromagnetic field modes in the context of cavity quantum electrodynamics [1]. In Ramsey atomic interferometry [2], in particular, they are known to generate quantum superpositions of atomic states as if the field inside them were of a classical nature. Two cavities separated by an intermediate region are filled with fields oscillating with phase coherence so that atomic transition probability amplitudes undergo quantum superpositions observed as interference (Ramsey) fringes. When this situation holds for temperatures close to absolute zero and field intensities of the order of a single photon, one may ask to what extent the quantum nature of the field can be neglected and how can this be theoretically modeled from basic quantum theory.In contrast to high-quality-factor cavities, in which photons dissipate at sufficiently low rates, the cavities used in such interferometric devices must be continuously pumped by an external source in order to make up for the relatively short photon lifetimes, if a stationary state is to be maintained in them. In this respect the cavity mode must be considered as a damped system. Open quantum systems have been the subject of renewed interest in many areas including quantum optics [3]. The interaction with a large external reservoir provides, within the standard quantum mechanical framework, one way of accounting for effective nonunitary dissipative subsystem dynamics [4], a characteristic of which is to act on the coherence properties of the subsystem states. Quantum coherence can be thereby destroyed [5], as is observed in most of the macroscopic world and theoretically expected also in a mesoscopic scale. Such decoherence processes often take place at very short time scales, so that they can be studied, in some models at least, by means of a perturbative short-time expansion for the coherence loss, which can be measured, e.g., by the so-called linear entropy (or idempotency defect) [6]. The progressive decoherence (due to the relatively small dissipation in the high-quality-factor cavity) of mesoscopic quantum superspositions of field coherent states ("Schrödinger cat states") has recently been experimentally observed...

We set up a semiclassical approximation which helps us clarify by means of several simple examples the rich variety of time scale in the quantum domain. The underlying structure of quantum and classical mechanics is so completly different that it is naive to expect to reach a classical regime by counting powers of the quantum scale variant Planck's over 2pi. We show although it is possible to define a time scale for nonclassical phenomena, but it is impossible to characterize quantum dynamics through a unique time scale, such as Ehrenfest's time. We use simple systems to critically discuss and illustrate these features of the quantum-classical limit.