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We theoretically investigate the impact of the excited state quantum phase transition on the adiabatic dynamics for the Lipkin-Meshkov-Glick model. Using a time dependent protocol, we continuously change a model parameter and then discuss the scaling properties of the system especially close to the excited state quantum phase transition where we find that these depend on the energy eigenstate. On top, we show that the mean-field dynamics with the time dependent protocol gives the correct scaling and expectation values in the thermodynamic limit even for the excited states.

We analyse the thermodynamic properties of a generalised Dicke model, i.e. a collection of three-level systems interacting with two bosonic modes. We show that at finite temperatures the system undergoes first-order phase transitions only, which is in contrast to the zero-temperature case where a second-order phase transition exist as well. We discuss the free energy and prominent expectation values. The limit of vanishing temperature is discussed as well.

We expand the standard thermodynamic framework of a system coupled to a thermal reservoir by considering a stream of independently prepared units repeatedly put into contact with the system. These units can be in any nonequilibrium state and interact with the system with an arbitrary strength and duration. We show that this stream constitutes an effective resource of nonequilibrium free energy and identify the conditions under which it behaves as a heat, work or information reservoir. We also show that this setup provides a natural framework to analyze information erasure ("Landauer's principle") and feedback controlled systems ("Maxwell's demon"). In the limit of a short system-unit interaction time, we further demonstrate that this setup can be used to provide a thermodynamically sound interpretation to many effective master equations. We discuss how non-autonomously driven systems, micromasers, lasing without inversion, and the electronic Maxwell demon, can be thermodynamically analyzed within our framework. While the present framework accounts for quantum features (e.g. squeezing, entanglement, coherence), we also show that quantum resources do not offer any advantage compared to classical ones in terms of the maximum extractable work., Comment: Final version. 28 pages incl. 9 figures + references

We provide an analytic solution to the problem of system-bath dynamics under the effect of high-frequency driving that has applications in a large class of settings, such as driven-dissipative many-body systems. Our method relies on discrete symmetries of the system-bath Hamiltonian and provides the time evolution operator of the full system, including bath degrees of freedom, without weak-coupling or Markovian assumptions. An interpretation of the solution in terms of the strobo- scopic evolution of a family of observables under the influence of an effective static Hamiltonian is proposed, which constitutes a flexible simulation procedure of non-trivial Hamiltonians. We instan- tiate the result with the study of the spin-boson model with time-dependent tunneling amplitude. We analyze the class of Hamiltonians that may be stroboscopically accessed for this example and illustrate the dynamics of system and bath degrees of freedom., Comment: Corrected minor typos in references

Non-equilibrium transport properties of quantum systems have recently become experimentally accessible in a number of platforms in so-called full-counting experiments that measure transient and steady state non-equilibrium transport dynamics. We show that the effect of the measurement back-action can be exploited to gain access to relevant transport coefficients. This relationship is general, but becomes most conspicuous in the transient dynamics of open quantum systems understrong coupling to non-Markovian environments. In order to explore this regime, a new simulation method for the generation of full counting statistics of non-Markovian, strong-coupling transport settings has been developed that is expressed in terms of a hierarchy of equations of motion. With this tool we gain access to the relevant regime and instantiate our proposal with the study of energetic conductance between two baths connected via a few level system., Comment: 7 pages, 3 figures; To appear in Phys. Rev. B

Feedback loops are known as a versatile tool for controlling transport in small systems, which usually have large intrinsic fluctuations. Here we investigate the control of a temporal correlation function, the waiting time distribution, under active and passive feedback conditions. We develop a general formalism and then specify to the simple unidirectional transport model, where we compare costs of open loop and feedback control and use methods from optimal control theory to optimize waiting time distributions., Comment: 15 pages, 6 figures. Minor corrections, new Fig 5a, additional reference. Accepted for publication in Phys. Rev. E

We propose a method to study the thermodynamic behaviour of small systems beyond the weak coupling and Markovian approximation, which is different in spirit from conventional approaches. The idea is to redefine the system and environment such that the effective, redefined system is again coupled weakly to Markovian residual baths and thus, allows to derive a consistent thermodynamic framework for this new system-environment partition. To achieve this goal we make use of the reaction coordinate mapping, which is a general method in the sense that it can be applied to an arbitrary (quantum or classical and even time-dependent) system coupled linearly to an arbitrary number of harmonic oscillator reservoirs. The core of the method relies on an appropriate identification of a part of the environment (the reaction coordinate), which is subsequently included as a part of the system. We demonstrate the power of this concept by showing that non-Markovian effects can significantly enhance the steady state efficiency of a three-level-maser heat engine, even in the regime of weak system-bath coupling. Furthermore, we show for a single electron transistor coupled to vibrations that our method allows one to justify master equations derived in a polaron transformed reference frame., Comment: updated and improved version; 19 pages incl. 10 figures and 5 pages appendix

A Markovian open quantum system which relaxes to a unique steady state $\rho_{ss}$ of finite rank can be decomposed into a finite physically realizable ensemble (PRE) of pure states. That is, as shown by Karasik and Wiseman [Phys. Rev. Lett. 106, 020406 (2011)], in principle there is a way to monitor the environment so that in the long time limit the conditional state jumps between a finite number of possible pure states. In this paper we show how to apply this idea to the dynamics of a double quantum dot arising from the feedback control of quantum transport, as previously considered by one of us and co-workers [Phys. Rev. B 84, 085302 (2011)]. Specifically, we consider the limit where the system can be described as a qubit, and show that while the control scheme can always realize a two-state PRE, in the incoherent tunneling regime there are infinitely many PREs compatible with the dynamics that cannot be so realized. For the two-state PREs that are realized, we calculate the counting statistics and see a clear distinction between the coherent and incoherent regimes., Comment: 11 pages, 4 figures

We study the excitation spectrum of a family of transverse-field spin chain models with variable interaction range and arbitrary spin $S$, which in the case of $S=1/2$ interpolates between the Lipkin-Meshkov-Glick and the Ising model. For any finite number $N$ of spins, a semiclassical energy manifold is derived in the large-$S$ limit employing bosonization methods, and its geometry is shown to determine not only the leading-order term but also the higher-order quantum fluctuations. Based on a multi-configurational mean-field ansatz, we obtain the semiclassical backbone of the quantum spectrum through the extremal points of a series of one-dimensional energy landscapes -- each one exhibiting a bifurcation when the external magnetic field drops below a threshold value. The obtained spectra become exact in the limit of vanishing or very strong external, transverse magnetic fields. Further analysis of the higher-order corrections in $1/\sqrt{2S}$ enables us to analytically study the dispersion relations of spin-wave excitations around the semiclassical energy levels. Within the same model, we are able to investigate quantum bifurcations, which occur in the semiclassical ($S\gg 1$) limit, and quantum phase transitions, which are observed in the thermodynamic ($N\rightarrow\infty$) limit., Comment: 20 pages, 13 figures

For the paradigmatic case of the damped quantum harmonic oscillator we present two measurement-based feedback schemes to control the stability of its fixed point. The first scheme feeds back a Pyragas-like time-delayed reference signal and the second uses a predetermined instead of time-delayed reference signal. We show that both schemes can reverse the effect of the damping by turning the stable fixed point into an unstable one. Finally, by taking the classical limit $\hbar\rightarrow0$ we explicitly distinguish between inherent quantum effects and effects, which would be also present in a classical noisy feedback loop. In particular, we point out that the correct description of a classical particle conditioned on a noisy measurement record is given by a non-linear stochastic Fokker-Planck equation and not a Langevin equation, which has observable consequences on average as soon as feedback is considered., Comment: To appear in "Control of Self-Organizing Nonlinear Systems" (conference proceedings, Springer-Verlag)

We investigate the dynamics of a two-mode laser system by extending the two-mode Tavis-Cummings model with dissipative channels and incoherent pumping and by applying the mean-field approximation in the thermodynamic limit. To this end we analytically calculate up to four possible non-equilibrium steady states (fixed points) and determine the corresponding complex phase diagram. Various possible phases are distinguished by the actual number of fixed points and their stability. In addition, we apply three time-delayed Pyragas feedback control schemes. Depending on the time delay and the strength of the control term this can lead to the stabilization of unstable fixed points or to the selection of a particular cavity mode that is macroscopically occupied.

In analogy to Brownian computers we explicitly show how to construct stochastic models, which mimic the behaviour of a general purpose computer (a Turing machine). Our models are discrete state systems obeying a Markovian master equation, which are logically reversible and have a well-defined and consistent thermodynamic interpretation. The resulting master equation, which describes a simple one-step process on an enormously large state space, allows us to thoroughly investigate the thermodynamics of computation for this situation. Especially, in the stationary regime we can well approximate the master equation by a simple Fokker-Planck equation in one dimension. We then show that the entropy production rate at steady state can be made arbitrarily small, but the total (integrated) entropy production is finite and grows logarithmically with the number of computational steps., Comment: 13 pages incl. appendix, 3 figures and 1 table, slightly changed version as published in PRE

We investigate the role of dissipation in excited state quantum phase transitions (ESQPT) within the Lipkin-Meshkov-Glick model. Signatures of the ESQPT are directly visible in the complex spectrum of an effective Hamiltonian, whereas they get smeared out in the time-dependence of system observables. In the latter case, we show how delayed feedback control can be used to restore the visibility of the ESQPT signals.

We investigate the thermodynamics of simple (non-interacting) transport models beyond the scope of weak coupling. For a single fermionic or bosonic level -- tunnel-coupled to two reservoirs -- exact expressions for the stationary matter and energy current are derived from the solutions of the Heisenberg equations of motion. The positivity of the steady-state entropy production rate is demonstrated explicitly. Finally, for a configuration in which particles are pumped upwards in chemical potential by a downward temperature gradient, we demonstrate that the thermodynamic efficiency of this process decreases when the coupling strength between system and reservoirs is increased, as a direct consequence of the loss of a tight coupling between energy and matter currents., Comment: 6 pages, 2 figures, to appear in EPL

A model for autonomous feedback control of particle transport through a large number of channels is introduced. Interactions among the particles can lead to a strong suppression of fluctuations in the particle number statistics. Within a mean-field type limit, the collective control mechanism becomes equivalent to a synchronization with an external clock. The diffusive spreading of the feedback signal across the channels shows scaling, can be quantified via the flow of information, and shows up, e.g., in the spectral function of the particle noise., Comment: 10 pages, 2 figures

We discuss singularities in the spectrum of driven many-body spin systems. In contrast to undriven models, the driving allows us to control the geometry of the quasienergy landscape. As a consequence, one can engineer singularities in the density of quasienergy states by tuning an external control. We show that the density of levels exhibits logarithmic divergences at the saddle points, while jumps are due to local minima of the quasienergy landscape. We discuss the characteristic signatures of these divergences in observables like the magnetization, which should be measurable with current technology., Comment: 10 pages, 4 figures, comments welcome

We study coherent transport through a double quantum dot. Its two electronic leads induce electronic matter and energy transport and a phonon reservoir contributes further energy exchanges. By treating the system-lead couplings perturbatively, whereas the coupling to vibrations is treated non-perturbatively in a polaron-transformed frame, we derive a thermodynamic consistent low-dimensional master equation. When the number of phonon modes is finite, a Markovian description is only possible when these couple symmetrically to both quantum dots. For a continuum of phonon modes however, also asymmetric couplings can be described with a Markovian master equation. We compute the electronic current and dephasing rate. The electronic current enables transport spectroscopy of the phonon frequency and displays signatures of Franck-Condon blockade. For infinite external bias but finite tunneling bandwidths, we find oscillations in the current as a function of the internal bias due to the electron-phonon coupling. Furthermore, we derive the full fluctuation theorem and show its identity to the entropy production in the system., Comment: 17 pages, 5 figures, shortened presentation, added references, to appear in JCP

We study the phenomenology of maximum-entropy meso-reservoirs, where we assume that their local thermal equilibrium state changes consistently with the heat transferred between the meso-reservoirs. Depending on heat and matter carrying capacities, the chemical potentials and temperatures are allowed to vary in time, and using global conservation relations we solve their evolution equations. We compare two-terminal transport between bosonic and fermionic meso-reservoirs via systems that tightly couple energy and matter currents and systems that do not. For bosonic reservoirs we observe the temporary formation of a Bose-Einstein condensate in one of the meso-reservoirs from an initial nonequilibrium setup., Comment: added appendices, to appear in NJP

Floquet Majorana Fermions appear as steady states at the boundary of time-periodic topological phases of matter. In this work, we theoretically study the main features of these exotic topological phases in the periodically driven one-dimensional Kitaev model. By controlling the ac fields, we can predict new topological phase transitions that should give rise to signatures of Majorana states in experiments. Moreover, the knowledge of the time-dependence of these Majorana states allows one to manipulate them. Our work contains a complete analysis of the monochromatic driving in different frequency regimes., Comment: 11 pages, 7 figures

We propose a physically realizable Maxwell's demon device using a spin valve interacting unitarily for a short time with electrons placed on a tape of quantum dots, which is thermodynamically equivalent to the device introduced by Mandal and Jarzynski [PNAS 109, 11641 (2012)]. The model is exactly solvable and we show that it can be equivalently interpreted as a Brownian ratchet demon. We then consider a measurement based discrete feedback scheme, which produces identical system dynamics, but possesses a different second law inequality. We show that the second law for discrete feedback control can provide a smaller, equal or larger bound on the maximum extractable work as compared to the second law involving the tape of bits. Finally, we derive an effective master equation governing the system evolution for Poisson distributed bits on the tape (or measurement times respectively) and we show that its associated entropy production rate contains the same physical statement as the second law involving the tape of bits., Comment: 13 pages, 6 figures

We analyze the equilibration process between two either fermionic or bosonic reservoirs containing ultracold atoms with a fixed total number of particles that are weakly connected via a few-level quantum system. We allow for both the temperatures and particle densities of the reservoirs to evolve in time. Subsequently, linearizing the resulting equations enables us to characterize the equilibration process and its time scales in terms of equilibrium reservoir properties and linear-response transport coefficients. Additionally, we investigate the use of such a device as particle transistor or particle capacitor and analyze its efficiency.

We present a theory of magnetotransport through an electronic orbital, where the electron spin interacts with a (sufficiently) large external spin via an exchange interaction. Using a semiclassical approximation, we derive a set of equations of motions for the electron density matrix and the mean value of the external spin that turns out to be highly nonlinear. The dissipation via the electronic leads is implemented in terms of a quantum master equation that is combined with the nonlinear terms of the spin-spin interaction. With an anisotropic exchange coupling a variety of dynamics is generated, such as self-sustained oscillations with parametric resonances or even chaotic behavior. Within our theory we can integrate a Maxwell-demon-like closed-loop feedback scheme that is capable of transporting particles against an applied bias voltage and that can be used to implement a spin filter to generate spin-dependent oscillating currents of opposite directions., Comment: 21 pages, 10 figures, comments are welcome, published in PRB

We consider bosonic transport through one-dimensional spin systems. Transport is induced by coupling the spin systems to bosonic reservoirs kept at different temperatures. In the limit of weak-coupling between spins and bosons we apply the quantum-optical master equation to calculate the energy transmitted from source to drain reservoirs. At large thermal bias, we find that the current for longitudinal transport becomes independent of the chain length and is also not drastically affected by the presence of disorder. In contrast, at small temperatures, the current scales inversely with the chain length and is further suppressed in presence of disorder. We also find that the critical behaviour of the ground state is mapped to critical behaviour of the current -- even in configurations with infinite thermal bias., Comment: 17 pages, 7 figures, minor changes (to appear in Journal of Physics, Condensed Matter)

We apply the time-delayed Pyragas control scheme to the dissipative Dicke model via a modulation of the atom-field-coupling. The feedback creates an infinite sequence of non-equilibrium phases with fixed points and limit cycles in the primary superradiant regime. We analyse this Hopf bifurcation scenario as a function of delay time and feedback strength, and determine analytical conditions for the phase boundaries.

We investigate the transport through a few-level quantum system described by a Markovian master equation with temperature- and particle-density dependent chemical potentials. From the corresponding Onsager relations we extract linear response transport coefficients in analogy to the electronic conductance, thermal conductance and thermopower. Considering ideal Fermi and Bose gas reservoirs we observe steady-state currents against the thermal bias as a result of the non-linearities introduced by the constraint of a constant particle density in the reservoirs. Most importantly, we find signatures of the on-set of Bose-Einstein condensation in the transport coefficients., Comment: 16 pages, 11 figures

We derive analytical results for various quantities related to the excited-state quantum phase transitions in a class of Dicke superradiance models in the semiclassical limit. Based on a calculation of a partition sum restricted to Dicke states, we discuss the singular behavior of the derivative of the density of states and find observables like the mean (atomic) inversion and the boson (photon) number and its fluctuations at arbitrary energies. Criticality depends on energy and a parameter that quantifies the relative weight of rotating versus counter-rotating terms, and we find a close analogy to the logarithmic and jump-type non-analyticities known from the Lipkin-Meshkov-Glick model., Comment: 14 pages, 3 figures

We consider open quantum systems weakly coupled to thermal reservoirs and subjected to quantum feedback operations triggered with or without delay by monitored quantum jumps. We establish a thermodynamic description of such system and analyze how the first and second law of thermodynamics are modified by the feedback. We apply our formalism to study the efficiency of a qubit subjected to a quantum feedback control and operating as a heat pump between two reservoirs. We also demonstrate that quantum feedbacks can be used to stabilize coherences in nonequilibrium stationary states which in some cases may even become pure quantum states., Comment: 12 pages, 6 figures

We theoretically propose optical phonon lasing in a double quantum dot (DQD) fabricated on a semiconductor substrate. No additional cavity or resonator is required. An electron in the DQD is found to be coupled to only two longitudinal optical phonon modes that act as a natural cavity. When the energy level spacing in the DQD is tuned to the phonon energy, the electron transfer is accompanied by the emission of the phonon modes. The resulting non-equilibrium motion of electrons and phonons is analyzed by the rate equation approach based on the Born-Markov-Secular approximation. We show that the lasing occurs for pumping the DQD via electron tunneling at rate much larger than the phonon decay rate, whereas a phonon antibunching is observed in the opposite regime of slow tunneling. Both effects disappear by an effective thermalization induced by the Franck-Condon effect in a DQD fabricated in a suspended carbon nanotube with strong electron-phonon coupling., Comment: 27 pages, 8 figures

We consider a driven single mode Dicke-Hamiltonian coupled to a dissipative zero-temperature bath. We derive the cumulant generating function for emitted photons of this quantum-critical system by using a $P$-representation of the master equation in the thermodynamic limit. This cumulant generating function is shown to consist of two parts: a macroscopic component, which is Poissonian in nature with characteristic rate proportional to the order parameter of the system; and a part describing fluctuations which is non-trivial in form and divergent around the quantum phase transition., Comment: 9 pages, 5 figures

We present a physical implementation of a Maxwell demon which consists of a conventional single electron transistor (SET) capacitively coupled to another quantum dot detecting its state. Altogether, the system is described by stochastic thermodynamics. We identify the regime where the energetics of the SET is not affected by the detection, but where its coarse-grained entropy production is shown to contain a new contribution compared to the isolated SET. This additional contribution can be identified as the information flow generated by the "Maxwell demon" feedback in an idealized limit., Comment: 4 pages, 3 figures, V2: as accepted in PRL + ref.[20]

We propose a possibility of a phonon laser by coupling a Bose-Einstein condensate to a nanomechanical cantilever with a magnetic tip. Due to the magnetic coupling, atomic spin flips induce cantilever motion which can be used to produce a phonon laser. The system is described by the equivalent of the Jaynes-Cummings Hamiltonian. By controlling the number of atoms and the population inversion, one can obtain either a continuous wave (cw) or transient lasing. The two-body atom-atom interaction is also shown to coherently manipulate the lasing process. We also show that in the strong coupling limit, the same system can undergo a Dicke-Hepp-Lieb superradiant phase transition. Exotic phase diagrams can be obtained by tuning the two body atom-atom interaction., Comment: comments welcome

We consider an ensemble of three-level particles in lambda-configuration interacting with two bosonic modes. The Hamiltonian has the form of a generalized Dicke-model. We show that in the thermodynamic limit this model supports a superradiant quantum phase transition. Remarkably, this can be both a first and a second order phase transition. A connection of the phase diagram to the symmetries of the Hamiltonian is also given. In addition, we show that this model can describe atoms interacting with an electromagnetic field in which the microscopic Hamiltonian includes a diamagnetic contribution. Even though the parameters of the atomic system respect the Thomas--Reiche--Kuhn sum rule, the system still shows a superradiant phase transition., Comment: 9 pages, 3 figures

We propose an all-electronic technique to manipulate and control interacting quantum systems by unitary single-jump feedback conditioned on the outcome of a capacitively coupled electrometer and in particular a single-electron transistor. We provide a general scheme to stabilize pure states in the quantum system and employ an effective Hamiltonian method for the quantum master equation to elaborate on the nature of stabilizable states and the conditions under which state purification can be achieved. The state engineering within the quantum feedback scheme is shown to be linked with the solution of an inverse eigenvalue problem. Two applications of the feedback scheme are presented in detail: (i) stabilization of delocalized pure states in a single charge qubit and (ii) entanglement stabilization in two coupled charge qubits. In the latter example we demonstrate the stabilization of a maximally entangled Bell state for certain detector positions and local feedback operations., Comment: 23 pages, 6 figures, to be published by New Journal of Physics (2013)

We present a transport setup of coupled quantum dots that enables the creation of spatially separated spin-entangled two-electron dark states. We prove the existence of an entangled transport dark state by investigating the system Hamiltonian without coupling to the electronic reservoirs. In the transport regime the entangled dark state which corresponds to a singlet has a strongly enhanced Fano factor compared to the dark state which corresponds to a mixture of the triplet states. Furthermore we calculate the concurrence of the occupying electrons to show the degree of entanglement in the transport regime., Comment: 9 pages and 3 figures

We consider thermal transport between two reservoirs coupled by a quantum Ising chain as a model for non-equilibrium physics induced in quantum-critical many-body systems. By deriving rate equations based on exact expressions for the quasiparticle pairs generated during the transport, we observe signatures of the underlying quantum phase transition in the steady-state energy current already at finite reservoir temperatures., Comment: to appear in PRL

We present a theory of magnetotransport through a system of two coupled electronic orbitals, where the electron spin interacts with a (large) local magnetic moment via an exchange interaction. For the physical realization of such a set-up we have in mind, for example, semiconductor quantum dots coupled to an ensemble of nuclear spins in the host material or molecular orbitals coupled to a local magnetic moment. Using a semiclassical approximation, we derive a set of Ehrenfest equations of motion for the electron density matrix and the mean value of the external spin (Landau equations): Due to the spin coupling they turn out to be nonlinear and, importantly, also coherences between electron states with different spin directions need to be considered. The electronic spin-polarized leads are implemented in form of a Lindblad-type dissipator in the infinite bias limit. We have solved this involved dynamical system numerically for various isotropic and anisotropic coupling schemes. For isotropic spin coupling and spin-polarized leads we study the effect of current-induced magnetization of the attached spin and compare this with a single quantum dot set-up. We further demonstrate that an anisotropic coupling can lead to a rich variety of parametric oscillations in the average current reflecting the complicated interplay between the Larmor precession of the external spin and the dissipative coherent dynamics of the electron spin., Comment: 10 pages, 6 figures, comments are welcome

For the multi-mode Dicke model in a transport setting that exhibits collective boson transmissions, we construct the equation of motion for the cumulant generating function. Approximating the exact system of equations at the level of cumulant generating function and system operators at lowest order, allows us to recover master equation results of the Full Counting Statistics for certain parameter regimes at very low cost of computation. The thermodynamic limit, that is not accessible with the master equation approach, can be derived analytically for different approximations., Comment: 7 pages, 3 figures, revised version, accepted by PRA

Using a simple quantum master equation approach, we calculate the Full Counting Statistics of a single electron transistor strongly coupled to vibrations. The Full Counting Statistics contains both the statistics of integrated particle and energy currents associated to the transferred electrons and phonons. A universal as well as an effective fluctuation theorem are derived for the general case where the various reservoir temperatures and chemical potentials are different. The first relates to the entropy production generated in the junction while the second reveals internal information of the system. The model recovers Franck-Condon blockade and potential applications to non-invasive molecular spectroscopy are discussed., Comment: extended discussion, to appear in NJP

We propose optical phonon lasing for a double quantum dot (DQD) fabricated in a semiconductor substrate. We show that the DQD is weakly coupled to only two LO phonon modes that act as a natural cavity. The lasing occurs for pumping the DQD via electronic tunneling at rates much higher than the phonon decay rate, whereas an antibunching of phonon emission is observed in the opposite regime of slow tunneling. Both effects disappear with an effective thermalization induced by the Franck-Condon effect in a DQD fabricated in a carbon nanotube with a strong electron-phonon coupling., Comment: 8 pages, 4 figures

We investigate the electronic transport through two parallel double quantum dots coupled both capacitively and via a perpendicularly aligned charge qubit. The presence of the qubit leads to a modification of the coherent tunnel amplitudes of each double quantum dot. We study the influence of the qubit on the electronic steady state currents through the system, the entanglement between the transport double quantum dots, and the back action on the charge qubit. We use a Born-Markov-Secular quantum master equation for the system. The obtained currents show signatures of the qubit. The stationary qubit state may be tuned and even rendered pure by applying suitable voltages. In the Coulomb diamonds it is also possible to stabilize pure entangled states of the transport double quantum dots.

In quantum optics the $g^{(2)}$-function is a standard tool to investigate photon emission statistics. We define a $g^{(2)}$-function for electronic transport and use it to investigate the bunching and anti-bunching of electron currents. Importantly, we show that super-Poissonian electron statistics do not necessarily imply electron bunching, and that sub-Poissonian statistics do not imply anti-bunching. We discuss the information contained in $g^{(2)}(\tau)$ for several typical examples of transport through nano-structures such as few-level quantum dots., Comment: 8 pages, 5 figures

We extend the second-order von Neumann approach within the generalized master equation formalism for quantum electronic transport to include the counting field. The resulting non-Markovian evolution equation for the reduced density matrix of the system resolved with respect to the number of transported charges enables the evaluation of the noise and higher-order cumulants of the full counting statistics. We apply this formalism to an analytically solvable model of a single-level quantum dot coupled to highly biased leads with Lorentzian energy-dependent tunnel coupling and demonstrate that, although reproducing exactly the mean current, the resonant tunneling approximation is not exact for the noise and higher order cumulants. Even if it may fail in the regime of strongly non-Markovian dynamics, this approach generically improves results of lower-order and/or Markovian approaches., Comment: 5 pages, 1 figure; little changes; very similar to the published version

We theoretically study an extension of the Dicke model, where the single-particle Hamiltonian has three energy levels in Lambda-configuration, i.e. the excited state is coupled to two non-degenerate ground states via two independent quantized light fields. The corresponding many-body Hamiltonian can be diagonalized in the thermodynamic limit with the help of a generalized Holstein--Primakoff transformation. Analyzing the ground-state energy and the excitation energies, we identify one normal and two superradiant phases, separated by phase transitions of both first and second order. A phase with both superradiant states coexisting is not stable. In addition, in the limit of two degenerate ground states a dark state emerges, which seems to be analogous to the dark state appearing in the well known stimulated Raman adiabatic passage scheme., Comment: 9 pages, 6 figures

We demonstrate the validity of the current fluctuation theorem for a double quantum dot surrounded by four terminals within the Born-, Markov- and secular approximations beyond the Coulomb-blockade regime. The electronic tunneling to two fermionic contacts conserves the total number of electrons, and the internal tunneling is phonon-assisted by two bosonic baths. Adapted choice of thermodynamic parameters between the baths may drive a current against an existing electric or thermal gradient. We study the apparent violation of the fluctuation theorem when only some of the energy and matter currents are monitored., Comment: 7 pages, 3 figures, added references, to appear in PRB

We suggest that a single-electron transistor continuously monitored by a quantum point contact may function as a Maxwell demon when closed-loop feedback operations are applied as time-dependent modifications of the tunneling rates across its junctions. The device may induce a current across the single-electron transistor even when no bias voltage or thermal gradient is applied. For different feedback schemes, we derive effective master equations and compare the induced feedback current and its fluctuations as well as the generated power. Provided that tunneling rates can be modified without changing the transistor level, the device may be implemented with current technology., Comment: 10 pages, 5 figures, more details added, to appear in PRB

We investigate non-linear magneto-transport through a single level quantum dot coupled to ferromagnetic leads, where the electron spin is coupled to a large, external (pseudo)spin via an anisotropic exchange interaction. We find regimes where the average current through the dot displays self-sustained oscillations that reflect the limit-cycles and chaos and map the dependence of this behaviour on magnetic field strength and the tunnel coupling to the external leads., Comment: 12 pages, 8 figures. Published version

We propose a feedback control scheme for generating and stabilizing pure states of transport devices, such as charge qubits, under non-equilibrium conditions. The purification of the device state is conditioned on single electron jumps and leaves a clear signal in the full counting statistics which can be used to optimize control parameters. As an example of our control scheme, we are presenting the stabilization pure transport states in a double quantum dot setup with the inclusion of phonon dephasing., Comment: 7 pages, 5 figures

We theoretically study cooperative effects in the steady-state transmission of photons through a medium of $N$ radiators. Using methods from quantum transport, we find a cross-over in scaling from $N$ to $N^2$ in the current and even higher powers of $N$ in the higher cumulants of the photon counting statistics as a function of the tunable source occupation. The effect should be observable for atoms confined within a nano-cell with a pumped optical cavity as photon source., Comment: extended results, 9 pages, 2 figures, to appear in Annals of Physics

The current through nanostructures like quantum dots can be stabilized by a feedback loop that continuously adjusts system parameters as a function of the number of tunnelled particles $n$. At large times, the feedback loop freezes the fluctuations of $n$ which leads to highly accurate, continuous single particle transfers. For the simplest case of feedback acting simultaneously on all system parameters, we show how to reconstruct the original full counting statistics from the frozen distribution., Comment: 4 pages, 2 figures

We study the combined counting statistics of two capacitively coupled transport channels. In particular, we examine the conditions necessary for utilizing one channel as detector sensitive to the occupation of the other. A good detector fidelity may be achieved in a bistable regime when the tunneling rates through the two channels are vastly different -- even when the physical back-action of the detector on the probed channel is large. Our methods allow to estimate the error of charge counting detectors from time-resolved current measurements -- which have been obtained in recent experiments -- alone., Comment: 4 pages, 3 figures, changed title, extensively re-organized version with improved presentation