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gernot.schaller@tu-berlin.de [4]
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Non-Markovianity and Strong Coupling Effects in Thermodynamics [7]

April 10 - April 13, 2017, Bad Honnef, Germany

We are glad to announce the 640. W. E. Heraeus Seminar on non-Markovianity and strong coupling effects in thermodynamics. Please find more information in our website [8].

Die Arbeitsgruppe beschäftigt sich zur Zeit stark mit Quantenkohärenz, Quantenoptik, und Vielteilchen-Effekten in niedrigdimensionalen Festkörperstrukturen. Ein wesentlicher Schwerpunkt ist die Schnittstelle zwischen elektronischem Transport und quantenoptischen Effekten. Uns interessiert ein breites Spektrum theoretischer Probleme, die von eher abstrakten Fragestellungen (z.B. der Definition quantenmechanischer Verschränkung in Vielteilchen-Systemen oder im Nichtgleichgewicht) über neue physikalische Modelle und Methoden (z.B. für nanomechanische Systeme) bis hin zu elektronischen, optischen und elastischen Materialeigenschaften (z.B. Phononen) reichen. Dementsprechend kommen verschiedene Techniken zum Einsatz - exakte Lösungen, rein numerische Berechnungen, und häufig Kombinationen analytischer und numerischer Methoden. Die Arbeitsgruppe ist an zahlreichen internationalen Kooperationen beteiligt, u.a. Madrid (R. Aguado, G. Platero, D. Marcos, R. Sanchez), Prag (T. Novotny), Tainan (Y.-N. Chen), Tokyo (N. Lambert).

The relationship of topological insulators and superconductors and the field of nonlinear dynamics is widely unexplored. To address this subject, we adopt the linear coupling geometry of the Su-Schrieffer-Heeger model, a paradigmatic example for a topological insulator, and render it nonlinearly in the context of superconducting circuits. As a consequence, the system exhibits topologically enforced bifurcations as a function of the topological control parameter, which finally gives rise to chaotic dynamics, separating phases that exhibit clear topological features.

 G. Engelhardt, M. Benito, G. Platero, and T. Brandes

PRL 118, 197702 (2017) [10], arxiv:1611.01467 [11]

Under non-equilibrium conditions, bosonic modes can become dynamically unstable with an exponentially growing occupation. On the other hand, topological band structures give rise to symmetry protected midgap states. In this letter, we investigate the interplay of instability and topology. Thereby, we establish a general relation between topology and instability under ac-driving. We apply our findings to create dynamical instabilities which are strongly localized at the boundaries of a finite-size system. As these localized instabilities are protected by symmetry, they can be considered as topological instabilities.

G. Engelhardt, M. Benito, G. Platero, T. Brandes

PRL 117, 045302 (2016) [13], arXiv:1512.07653 [14] 

On top of the mean-field analysis of a Bose-Einstein condensate, one typically applies the Bogoliubov theory to analyze quantum fluctuations of the excited modes. Therefore, one has to diagonalize the Bogoliubov Hamiltonian in a symplectic manner. In our article, we investigate the topology of these Bogoliubov excitations in inversion-invariant systems of interacting bosons in one dimension. We analyze, how the condensate influences the topology of the Bogoliubov excitations. Analogously to the fermionic case, we here establish a symplectic extension of the polarization characterizing the topology of the Bogoliubov excitations and link it to the eigenvalues of the inversion operator at the inversion-invariant momenta. We also demonstrate at an instructive, but experimentally feasible example that this quantity is also related to edge states in the excitation spectrum.

G. Engelhardt and T. Brandes

Phys. Rev. A91 053621 (2015), [16]arXiv:1503.02503 [17]

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.

W. Kopylov, C. Emary, E. Schöll, and T. Brandes

New J. Phys. 17 013040 (2015), [19]arXiv:1403.0620 [20]

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.

F. G.-Marcos, G. Platero, C. Nietner, G. Schaller, and T. Brandes

Phys.Rev.A 90 033614 (2014), [22]arXiv:1407.2804 [23]

We investigate precursors of critical behavior in the quasienergy spectrum due to the dynamical instability in the kicked top. Using a semiclassical approach, we analytically obtain a logarithmic divergence in the density of states, which is analogous to a continuous excited state quantum phase transition in undriven systems. We propose a protocol to observe the cusp behavior of the magnetization close to the critical quasienergy.

V. M. Bastidas, P. Perez-Fernandez, M. Vogl, T. Brandes

Phys.Rev.Lett. [25] 112, arXiv:1308.5640 [26]

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 nonlinearities introduced by the constraint of a constant particle density in the reservoirs. Most importantly, we find signatures of the onset of Bose-Einstein condensation in the transport coefficients.

C. Nietner, G. Schaller, T. Brandes

Phys.Rev.A 89 013605 (2014), [28]arXiv:1309.3488 [29]

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.

P. Strasberg, G. Schaller, T. Brandes, and M. Esposito

Phys. Rev. Lett. 110, 040601 (2013), [31] arXiv:1210.5661 [32]

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.

M. Vogl, G. Schaller, T. Brandes

Phys. Rev. Lett 109, 240402 (2012) [34]

arXiv:1208.5989 [35]

We establish a set of nonequilibrium quantum phase transitions in the Dicke model by considering a monochromatic nonadiabatic modulation of the atom-field coupling. For weak driving the system exhibits a set of side-bands which allow the circumvention of the no-go theorem which otherwise forbids the occurence of superradiant phase transitions. At strong driving we show that the system exhibits a rich multistable structure and exhibits both first- and second-order nonequilibrium quantum phase transitions.

V. M. Bastidas, C. Emary, B. Regler, T. Brandes
Physical Review Letters 108, 043003 (2012) [37]
arXiv:1108.2987 [38]

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.

C. Nietner, G. Schaller, C. Pöltl, and T. Brandes

Physical Review B 85, 245431 (2012) [40]
arXiv:1204.2978 [41]

We investigate non-linear magneto-transport through a single level quantum dot 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.

C. Lopez-Monis, C. Emary, G. Kiesslich, G. Platero, and T. Brandes

Physical Review B 85, 045301 (2012) [43]
arXiv:1104.3995 [44]

We compare the semiclassical description of nanoelectromechanical systems (NEMS) within and beyond the adiabatic approximation. We consider a NEMS model that contains a single phonon (oscillator) mode linearly coupled to an electronic few-level system in contact with external particle reservoirs (leads). Using Feynman-Vernon influence functional theory, we derive a Langevin equation for the oscillator trajectory that is nonperturbative in the system-leads coupling. A stationary electronic current through the system generates nontrivial dynamical behavior of the oscillator, even in the adiabatic regime. The “ backaction” of the oscillator onto the current is studied as well. For the two simplest cases of one and two coupled electronic levels, we discuss the differences between the adiabatic and the nonadiabatic regime of the oscillator dynamics.

Anja Metelmann and Tobias Brandes
Physical Review B 84, 155455 (2011) [46]
arXiv:1107.3762 [47]

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.

Gernot Schaller, Clive Emary, Gerold Kiesslich, and Tobias Brandes
Physical Review B 84, 085418 (2011) [49]
arXiv:1106.4670 [50]

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 to 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.

Malte Vogl, Gernot Schaller, and Tobias Brandes
Ann. Phys. (N.Y.) 326, 2827 (2011) [52]
arXiv:1010.4416 [53]

We propose the manipulation of an isolated qubit by a simple instantaneous closed-loop feedback scheme in which a time-dependent electronic detector current is directly back-coupled into qubit parameters. As specific detector model we employ a capacitively coupled single-electron transistor. We demonstrate the stabilization of pure delocalized qubit states above a critical detector-qubit coupling. This electronic purification is independent of the initial qubit state and is accomplished after few electron jumps through the detector. Our simple scheme can be used for the efficient and robust initialization of solid-state qubits in quantum computational algorithms at arbitrary temperatures.

Gerold Kiesslich, Gernot Schaller, Clive Emary, and Tobias Brandes
Physical Review Letters 107, 050501 (2011) [55]
arXiv:1102.3771 [56]

For open quantum systems coupled to a thermal bath at inverse temperature β, it is well known that under the Born, Markov, and secular approximations, the system density matrix will approach the thermal Gibbs state with the bath inverse temperature β. We generalize this to systems where there exists a conserved quantity (e.g., the total particle number), where for a bath characterized by inverse temperature β and chemical potential μ, we find equilibration of both temperature and chemical potential. For couplings to multiple baths held at different temperatures and different chemical potentials, we identify a class of systems that equilibrates according to a single hypothetical average but in general nonthermal bath, which may be exploited to generate desired nonthermal states. Under special circumstances, the stationary state may again be described by a unique Boltzmann factor. These results are illustrated by several examples.

Gernot Schaller
Physical Review E 83, 031111 (2011) [58]
arXiv:1010.3094 [59]

We investigate the dynamics of a single phonon (oscillator) mode linearly coupled to an electronic few-level system in contact with external particle reservoirs (leads). A stationary electronic current through the system generates nontrivial dynamical behavior of the oscillator. Using Feynman-Vernon influence functional theory, we derive a Langevin equation for the oscillator trajectory that is nonperturbative in the system-leads coupling and from which we extract effective oscillator potentials and friction coefficients. For the two simplest cases of a single and two coupled electronic levels, we discuss various regimes of the oscillator dynamics.

R. Hussein, A. Metelmann, P. Zedler, and T. Brandes
Phys. Rev. B 82, 165406 (2010) [61]
arXiv:1006.2076 [62]

The current through nanostructures like quantum dots can be stabilized by a classical 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.

Tobias Brandes
Phys. Rev. Lett. 105, 060602 (2010) [64]
arXiv:1005.0018 [65]

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.

Gernot Schaller, Gerold Kiesslich, and Tobias Brandes
Phys. Rev. B 82, 041303(R) (2010) [67]
arXiv:1004.2604 [68]

We consider the question of how to distinguish quantum from classical transport through nanostructures. To address this issue we have derived two inequalities for temporal correlations in nonequilibrium transport in nanostructures weakly coupled to leads. The first inequality concerns local charge measurements and is of general validity; the second concerns the current flow through the device and is relevant for double quantum dots. Violation of either of these inequalities indicates that physics beyond that of a classical Markovian model is occurring in the nanostructure.

Neill Lambert, Clive Emary, Yueh-Nan Chen, Franco Nori
Phys. Rev. Lett. 105 176801 (2010) [70]
arXiv:1002.3020 [71]
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