We explore the prospects to control by use of time-dependent fields quantum transport phenomena in nanoscale systems. In particular, we study for driven conductors the electron current and its noise properties. We review recent corresponding theoretical descriptions which are based on Floquet theory. Alternative approaches, as well as various limiting approximation schemes are investigated and compared. The general theory is subsequently applied to different representative nanoscale devices, like the non-adiabatic pumps, molecular gates, molecular quantum ratchets, and molecular transistors. Potential applications range from molecular wires under the influence of strong laser fields to microwave-irradiated quantum dots.Comment: 82 pages, 19 figures, elsart.cls, solved LaTeX/hyperref problem

Using the parametrically driven harmonic oscillator as a working example, we study two different Markovian approaches to the quantum dynamics of a periodically driven system with dissipation. In the simpler approach, the driving enters the master equation for the reduced density operator only in the Hamiltonian term. An improved master equation is achieved by treating the entire driven system within the Floquet formalism and coupling it to the reservoir as a whole. The different ensuing evolution equations are compared in various representations, particularly as Fokker-Planck equations for the Wigner function. On all levels of approximation, these evolution equations retain the periodicity of the driving, so that their solutions have Floquet form and represent eigenfunctions of a non-unitary propagator over a single period of the driving. We discuss asymptotic states in the long-time limit as well as the conservative and the high-temperature limits. Numerical results obtained within the different Markov approximations are compared with the exact path-integral solution. The application of the improved Floquet-Markov scheme becomes increasingly important when considering stronger driving and lower temperatures. 42.50.Lc, 03.65.Sq Typeset using REVT E X † Present address:

We calculate the exact Landau-Zener transitions probabilities for a qubit with arbitrary linear coupling to a bath at zero temperature. The final quantum state exhibits a peculiar entanglement between the qubit and the bath. In the special case of a diagonal coupling, the bath does not influence the transition probability, whatever the speed of the Landau-Zener sweep. It is proposed to use Landau-Zener transitions to determine both the reorganization energy and the integrated spectral density of the bath. Possible applications include circuit QED and molecular nanomagnets.PACS numbers: 32.80. Bx, 74.50.+r, 32.80.Qk, 03.67.Lx Quite a number of quantum two-state systems are presently tested as candidate qubits, the units of quantum information. Good qubits are well isolated from their environment, but easy to manipulate. This somewhat conflicting requirement has spurred renewed interest in the dynamics of qubits coupled to an environment or heat bath [1,2]. Qubits can be seen as bath detectors. For example, static qubits probe via their decay rates the bath spectral density at their transition frequencies. In solid-state environments these rates can be strongly frequency-and sample-dependent. We discuss an in this respect superior 'bath detection mode' of the qubit.One way of changing the state of a two-level system involves the forced crossing of its diabatic energies. For constant level-crossing speed this is known as the Landau-Zener (LZ) problem [3,4,5], which for a twolevel system can be solved exactly [3,4,5,6]. This is no longer the case when taking its environment into account [7,8,9, 10] that may cause thermal excitation and quantum tunneling. In the low-temperature tunneling regime, analytical estimates for transition probabilities exist only for very fast and very slow sweeps, and the literature is not unanimous about the latter limit [7,8,9,10,11].In another line of research, incited by the paper [12], it was recently proven that LZ transition probabilities can be calculated exactly for some many-level systems as well, although only for some initial states [13,14,15,16]. In this Letter, we extend the analysis to quantum dissipative systems and study LZ transitions in spin-boson problems in a new way. First we calculate zero-temperature LZ transition probabilities exactly. Second, by making use of this exact dependence on the bath parameters, we propose to gauge the dissipative environment of a qubit by performing LZ sweeps. One advantage of this bath detection mode of the qubit is that effects of spiky bath spectral densities are averaged out in every sweep.Driven spin-boson model.-Consider LZ transitions in a qubit coupled to a bath of N quantum harmonic oscillators, as described by the Hamiltonianwith the qubit-oscillator coupling. (2) The energy difference between the diabatic qubit states changes linearly in time as vt (with level-crossing speed v > 0) and their intrinsic interaction amplitude is ∆. The σ x,z are Pauli operators. The first two terms of (1) define the standard Landau-Zener proble...

We generalize the dispersive theory of the Jaynes-Cummings model beyond the frequently employed rotating-wave approximation ͑RWA͒ in the coupling between the two-level system and the resonator. For a detuning sufficiently larger than the qubit-oscillator coupling, we diagonalize the non-RWA Hamiltonian and discuss the differences to the known RWA results. Our results extend the regime in which dispersive qubit readout is possible. If several qubits are coupled to one resonator, an effective qubit-qubit interaction of Ising type emerges, whereas RWA leads to isotropic XY interaction. This impacts on the entanglement characteristics of the qubits.

The effect of laser fields on electron transport through a molecular wire weakly coupled to two leads is investigated. The molecular wire acts as a coherent quantum ratchet if the molecule is composed of periodically arranged, asymmetric chemical groups. This setup presents a quantum rectifier with a finite dc response in the absence of a static bias. The nonlinear current is evaluated in closed form within the Floquet basis of the isolated, driven wire. The current response reveals multiple current reversals together with a nonlinear dependence on the amplitude and the frequency of the laser field. The current saturates for long wires at a nonzero value, while it may change sign upon decreasing its length.

The theory for current fluctuations in ac-driven transport through nanoscale systems is put forward. By use of a generalized, non-Hermitian Floquet theory we derive novel explicit expressions for the time-averaged current and the zero-frequency component of the power spectrum of current fluctuations. A distinct suppression of both the zero-frequency noise and the dc-current occurs for suitably tailored ac-fields. The relative level of transport noise, being characterized by a Fano factor, can selectively be manipulated by ac-sources; in particular, it exhibits both characteristic maxima and minima near current suppression.PACS numbers: 05.60. Gg, 85.65.+h, 72.40.+w Recent experimental successes in the coherent coupling of quantum dots [1] and in the reproducible measurement of electronic currents through molecules [2,3] have given rise to renewed theoretical interest in the transport properties of nanoscale systems [4,5]. Thereby, new ideas in order to exploit the quantum coherence of such systems for the construction of novel electronic devices [5] have emerged. One possible construction element is based on the manipulation of quantum dots or single molecules by use of an oscillating gate voltage or an infrared laser, respectively. A prominent effect of such ac-fields consists in the adiabatic [6,7,8,9] and nonadiabatic [10, 11] pumping of electrons. Moreover, laser irradiated molecular wires provide novel devices such as coherent quantum rectifiers [12] and optically controlled transistors [13]. However, such time-dependent control schemes can be valuable in practice only if they operate at tolerable noise levels. Thus, the question whether noise properties of nanoscale systems can be selectively manipulated becomes of foremost interest.Electron transport through time-independent, mesoscopic systems is commonly described within the framework of a scattering formalism. Both the average current [14] and the transport noise characteristics [15,16] can be expressed in terms of the quantum transmission coefficients for the corresponding transport channels. By contrast, the theory for driven quantum transport is much less developed. Expressions for the spectral density of the current fluctuations have been derived for the low-frequency ac-conductance [17] and the scattering by a slowly time-dependent potential [18]. However, the situation becomes more opaque in the presence of rapidly varying time-dependent fields. Within a Green function approach, a formal expression for the current through a time-dependent conductor has been presented in Refs. [19,20]. Here, we derive explicit expressions for both the current and the noise properties of electron transport through a nanoscale conductor under the influence of time-dependent forces at arbitrary frequency and strength. The dynamics of the electrons is solved by integrating the Heisenberg equations of motion for the electron creation/annihilation operators within a generalized Floquet approach. We then use the resulting expressions to explore the possibility of an ...

We study Landau-Zener transitions in a qubit coupled to a bath at zero temperature. A general formula is derived that is applicable to models with a non-degenerate ground state. We calculate exact transition probabilities for a qubit coupled to either a bosonic or a spin bath. The nature of the baths and the qubit-bath coupling is reflected in the transition probabilities. For diagonal coupling, when the bath causes energy fluctuations of the diabatic qubit states but no transitions between them, the transition probability coincides with the standard LZ probability of an isolated qubit. This result is universal as it does not depend on the specific type of bath. For pure offdiagonal coupling, by contrast, the tunneling probability is sensitive to the coupling strength. We discuss the relevance of our results for experiments on molecular nanomagnets, in circuit QED, and for the fast-pulse readout of superconducting phase qubits.

We study the influence of laser radiation on the electron transport through a molecular wire weakly coupled to two leads. In the absence of a generalized parity symmetry, the molecule rectifies the laser induced current, resulting in directed electron transport without any applied voltage. We consider two generic ways of dynamical symmetry breaking: mixing of different harmonics of the laser field and molecules consisting of asymmetric groups. For the evaluation of the nonlinear current, a numerically efficient formalism is derived which is based upon the Floquet solutions of the driven molecule. This permits a treatment in the non-adiabatic regime and beyond linear response.Comment: 12 pages, 10 figures, REVTeX