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# Statistical Mechanics of Quantum Dynamics

Europe/Stockholm
Mariehamn, Åland

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Description

### Venue

Mariehamn, Åland.

The venue is Hotel Arkipelag in Mariehamn, the capital of the province of Åland, Finland. The location is easily reachable by ferry from Stockholm, Turku (Finland), or Helsinki. There are also daily flights from Sweden and Finland.

### Scope

Recent years have seen a resurgence of interest in statistical mechanics aspects of quantum systems that are not covered by the well-developed quantum statistical mechanics. Key motivational questions have been quantum fluctuation relations and the generalization to the quantum domain of key concepts of non-equilibrium thermodynamics such as heat and work, all still actively investigated and where little consensus has been reached. The topic has many potential applications related to optimizing and control of quantum dynamics through interaction with the environment and through measurement. The workshop aims to bring together pioneers and leading researchers active in the field, and is also run as a school aimed at graduate and undergraduate students.

### Format

The workshop will start on the afternoon ferry from Stockholm on Wednesday, May 25, and end at lunch time on Saturday, May 28.

### Program

There is no workshop fee. Travel on the ferry from Stockholm to Mariehamn, including dinner on the ferry, is free for all participants, as are coffee and lunches at the workshop. We also plan for a workshop dinner on Thursday May 26.

The conference begins on Viking Line ferry sailing from Stockholm harbour May 25 2016, at 16.30 Swedish time. These large ferries leave sharply on time -- and wait for nobody. It is recommended that you be in the ferry terminal at 15.45, at the latest. Persons from the organizing committee will be in the ferry terminal with the tickets from 15.15, at the latest. A map of and travel directions to the ferry terminal can be found here.

### Invited speakers

 Michele Campisi, Pisa Raphael Chetrite, Nice and Helsinki Sergio Ciliberto, ENS-Lyon Christian Flindt, Aalto Francesco Giazotto, Pisa Frank Hekking, Grenoble Benjamin Huard, ENS-Paris Jorge Kurchan, ENS-Paris Klaus Mølmer, Aarhus Peter Reimann, Bielefeld Sorin Paraoanu, Aalto

### Application

If you want to apply for participation in the workshop, please fill in the application form. You will be informed by the organizers shortly after the application deadline whether your application has been approved. Due to space restrictions, the total number of participants is limited (40 slots are foreseen, invited speakers are of course automatically approved, but need to register anyway.)

There is no registration fee.

### Travel Reimbursement

PhD students and young Postdoc fellows are eligible for travel grants to participate in the program. If you are interested in such a grant, please mark the corresponding field in the application form, briefly summarize your interest in the program in the comments field, and indicate an estimation of your expected travel expenses. Since only a limited number of grants is available, decision concerning the grants will be made on a case-by-case basis and you will be notified shortly after the application deadline.

### Accommodation

From the registration page you may book a room at one of the two hotels we have reserved for the participants. This accommodation is to be paid on spot. You may also book your accommodation in Mariehamn yourself.

The event is supported by Nordita, by the Centre for Quantum Materials (KTH, Sweden), and by the Centre for Quantum Engineering (Aalto University, Finland).

• Wednesday, 25 May
• 17:00 19:00
Ferry session
• 17:00
Typical fast thermalization processes in closed many-body systems 45m
Lack of knowledge about the detailed many-particle motion on the microscopic scale is a key issue in any theoretical description of a macroscopic experiment. For systems at or close to thermal equilibrium, statistical mechanics provides a very successful general framework to cope with this problem. Far from equilibrium, only very few quantitative and comparably universal results are known. Here, a new quantum mechanical prediction of this type is derived and verified against various experimental and numerical data from the literature. It quantitatively describes the entire temporal relaxation towards thermal equilibrium for a large class (in a mathematically precisely defined sense) of closed many-body systems, whose initial state may be arbitrarily far from equilibrium.
Speaker: Peter Reimann (Bielefeld)
• 17:45
Novel order in driven Dirac materials 45m
Speaker: Christopher Triola (Nordita)
• Thursday, 26 May
• 09:00 12:00
Thursday morning
• 09:00
A protocol for reaching equilibrium arbitrary fast 45m
When a control parameter of a system is suddenly changed, the accessible phase space changes too and the system needs its characteristic relaxation time to reach the final equilibrium distribution. An important and relevant question is whether it is possible to travel from an equilibrium state to another in an arbitrary time, much shorter than the natural relaxation time. Such strategies are reminiscent of those worked out in the recent field of Shortcut to Adiabaticity, that aim at developing protocols, both in quantum and in classical regimes, allowing the system to move as fast as possible from one equilibrium position to a new one, provided that there exist an adiabatic transformation relating the two. Proof of principle experiments have been carried out for isolated systems. Instead in open system the reduction of the relaxation time, which is frequently desired and necessary, is often obtained by complex feedback processes. In this talk, we present a protocol,named Engineered Swift Equilibration (ESE), that shortcuts time-consuming relaxations. We tested experimentally this protocol on a Brownian particle trapped in an optical potential first and then on an AFM cantilever. We show that applying a specific driving, one can reach equilibrium in an arbitrary short time. We also estimate the energetic cost to get such a time reduction. Beyond its fundamental interest, the ESE method paves the way for applications in micro and nano devices, in high speed AFM, or in monitoring mesoscopic chemical or biological process. References: (1) Engineered Swift Equilibration, Ignacio A Martinez; Artyom Petrosyan; David Gully-Odelin; Emmanuel Trizac; Sergio Ciliberto, to be published in Nature Physics (2) Arbitrary fast modulation of an atomic force microscope, Anne Le Cunuder; Ignacio A Martinez; Artyom Petrosyan; David Gully-Odelin; Emmanuel Trizac; Sergio Ciliberto. Submitted to Applied Letters.
Speaker: Prof. Sergio Ciliberto (ENS-Lyon)
• 09:45
Engineered dissipative reservoirs for superconducting circuits 30m
Speaker: Prof. Mikko Möttönen (Aalto)
• 10:15
break 30m
• 10:45
Adiabatic state control in a three-level system 45m
The adiabatic manipulation of quantum states is a powerful technique from quantum optics and atomic physics. Previous work on the Autler-Townes effect in superconducting phase qutrits [1], on Stueckelberg interference [2], and on the effect of motional averaging in transmons [3] has added evidence that superconducting circuits truly behave as controllable artificial atoms. Here we benchmark the stimulated Raman adiabatic passage process for circuit quantum electrodynamics, by using the first three levels of a transmon qubit [4]. To realize this coherent transfer, we use two adiabatic Gaussian-shaped control microwave pulses coupled to the first and the second transition. In this ladder configuration, we measure a population transfer efficiency above 80% between the ground state and the second excited state. The advantage of this technique is robustness against errors in the timing of the control pulses. By doing quantum tomography at successive moments during the Raman pulses, we investigate the transfer of the population in time-domain. We also show that this protocol can be reversed by applying a third adiabatic pulse. Furthermore, we study the effect of applying the adiabatic Raman sequence to a superposition between the ground and the first excited state, and we present experimental results for the case of a quasi-degenerate intermediate level. The result is one step towards the realization of holonomic quantum computing and quantum simulators with superconducting circuits [5].
References:
[1] Mika A. Sillanpää, et. al., Phys. Rev. Lett. 103, (2009) 193601; Jian Li et. al., Phys. Rev. B 84, (2011) 104527; Jian Li et. al. , Sci. Rep. 2, 645 (2012).
[2] M.P. Silveri, K.S. Kumar, J. Tuorila, J. Li, A. Vepsäläinen, E.V. Thuneberg, G.S. Paraoanu, New J. Phys. 17, 043058 (2015).
[3] Jian Li, M. P. Silveri, K. S. Kumar, J.-M. Pirkkalainen, A. Vepsäläinen, W. C. Chien, J. Tuorila, M. A. Sillanpää, P. J. Hakonen, E. V. Thuneberg, G. S. Paraoanu, Nat. Commun. 4, 1420 (2013).
[4] K. S. Kumar, A. Vepsalainen, S. Danilin, G. S. Paraoanu, Nat. Commun. 7, 10628 (2016).
[5] G. S. Paraoanu, Recent progress in quantum simulation using superconducting circuits, J. Low. Temp. Phys. 175, 633-654 (2014) .
Speaker: Prof. Sorin Paraoanu (Aalto)
• 11:30
Single quantum level electron turnstile 30m
We report on the realization of a single-electron source, where current is transported through a single-level quantum dot (Q) tunnel coupled to two superconducting leads (S). When driven with an ac gate voltage, the experiment demonstrates electron turnstile operation. Compared to the more conventional superconductor–normal-metal–superconductor turnstile, our superconductor–quantum-dot– superconductor device presents a number of novel properties, including higher immunity to the unavoidable presence of nonequilibrium quasiparticles in superconducting leads. Moreover, we demonstrate its ability to deliver electrons with a very narrow energy distribution. In the second part of the talk I will discuss possible effects that go beyond the semi-classical picture, associated to the quantum dynamics of the quantum dot level coupled to the semi-continuum in the leads' DOS.
Speaker: Prof. Clemens Winkelmann (Grenoble)
• 16:00 17:30
Thursday afternoon
• 16:45
On-chip autonomous Maxwell's demon as an information-powered refrigerator 30m
Speaker: Dr Ivan Khaymovich (Grenoble)
• 17:15
break 15m
• 17:30 19:00
Poster session
• Friday, 27 May
• 09:00 12:15
Friday morning
• 09:00
The power of a critical heat engine 45m
Since its inception about two centuries ago thermodynamics has sparkled continuous interest and fundamental questions. According to the second law no heat engine can have an efficiency larger than Carnot’s efficiency. The latter can be achieved by the Carnot engine, which however ideally operates in infinite time, hence delivers null power. A currently open question is whether the Carnot efficiency can be achieved at finite power. Most of the previous works addressed this question within the Onsager matrix formalism of linear response theory. Here we pursue a different route based on finite-size-scaling theory. We focus on quantum Otto engines and show that when the working substance is at the verge of a second order phase transition diverging energy fluctuations can enable approaching the Carnot point without sacrificing power. The rate of such approach is dictated by the critical indices, thus showing the universal character of our analysis.
Nature Communications, in press (2016) arXiv:1603.05024
Speaker: Prof. Michele Campisi (Scuola Normale Superiore)
• 09:45
Extracting work with a superconducting qubit using a Maxwell demon 45m
Quantum thermodynamics of information addresses the link between information and energy in the quantum regime. Entanglement and measurement backaction are known to deeply affect information processing and their impact on quantum thermodynamics has attracted a lot of theoretical activity. A basic illustration of these ideas consists in devising a quantum version of the Maxwell demon that uses information on a system to extract work from it. In this talk, we will discuss an elementary thermal machine able to extract work from a superconducting quantum bit from the knowledge it acquires. We have realized such a machine using superconducting circuits in two manners. First, by measurement based feedback, a macroscopic observer acquires information about the quantum system and reacts on it. Second, using a microwave mode as a quantum Maxwell demon, we are able to directly measure the extracted work from a thermalized qubit. We track quantitatively the flows of energy and entropy at any step of the process owing to the high level of controllability of superconducting circuits. When the qubit starts in a coherent superposition, this work gives a direct picture of the power flows out of a qubit during coherent evolution and a measurement.
Speaker: Prof. Benjamin Huard (Ecole Normale Supérieure)
• 10:30
break 30m
• 11:00
Giant mesoscopic fluctuations of the elastic cotunneling thermopower of a single-electron transistor 45m
We study the thermoelectric transport of a small metallic island weakly coupled to two electrodes by tunnel junctions. In the Coulomb blockade regime, in the case when the ground state of the system corresponds to an even number of electrons on the island, the main mechanism of electron transport at lowest temperatures is elastic cotunneling. In this regime, the transport coefficients strongly depend on the realization of the random impurity potential or the shape of the island. Using the random-matrix theory, we calculate the thermopower and the thermoelectric kinetic coefficient and study the statistics of their mesoscopic fluctuations in the elastic cotunneling regime. The fluctuations of the thermopower turn out to be much larger than the average value.
Speaker: Prof. Frank Hekking (Grenoble)
• 11:45
Quantum Phase Slip Noise 30m
Quantum phase slips (QPS) generate voltage fluctuations in superconducting nanowires. Employing Keldysh technique and making use of the phase-charge duality arguments we develop a theory of QPS-induced voltage noise in such nanowires. We demonstrate that quantum tunneling of the magnetic flux quanta across the wire yields quantum shot noise which obeys Poisson statistics and is characterized by a power law dependence of its spectrum on the external bias. In the long wire limit noise spectrum decreases with increasing frequency and vanishes beyond a threshold value of frequency in the zero temperature limit. Our predictions can be directly tested in future experiments with superconducting nanowires.
Speaker: Prof. Andrew Semenov (P.N. Lebedev Physics Institute)
• 16:00 19:00
Friday afternoon
• 16:00
Superconducting phase-coherent caloritronics 45m
The Josephson effect [1] represents perhaps the prototype of macroscopic phase coherence and is at the basis of the most widespread interferometer, i.e., the superconducting quantum interference device (SQUID). Yet, in analogy to electric interference, Maki and Griffin [2] predicted in 1965 that thermal current flowing through a temperature-biased Josephson tunnel junction is a stationary periodic function of the quantum phase difference between the superconductors. In this scenario, a temperature-biased SQUID would allow heat currents to interfere thus implementing the thermal version of the electric Josephson interferometer.
In this talk I will initially report the first experimental realization of such a heat interferometer [3]. We investigate heat exchange between two normal metal electrodes kept at different temperatures and tunnel-coupled to each other through a thermal device in the form of a DC-SQUID. Heat transport in the system is found to be phase dependent, in agreement with the original prediction. After this initial demonstration, we have extended the concept of the heat interferometry to various other devices and functionalities, implementing the first quantum diffractor’ for thermal flux [4, 5], the realization of the first balanced Josephson heat modulator [6], and an ultra-efficient low-temperature hybrid heat current rectifier’ [7, 8], thermal counterpart of the well-known electric diode. In the latter, we demonstrate temperature differences exceeding 60 mK between the forward and reverse thermal bias configurations [9]. This structure offers a remarkably large heat rectification ratio up to about 140 and allows its prompt implementation in true solid-state thermal nanocircuits and general-purpose electronic applications requiring energy harvesting or thermal management and isolation at the nanoscale. Finally, I will conclude by showing the realization of a fully superconducting heat modulator based on the first tunable „0-π“ thermal Josephson junction.
References
[1] B. D. Josephson, Phys. Lett. 1, 251 (1962).
[2] K. Maki and A. Griffin, Phys. Rev. Lett. 15, 921 (1965).
[3] F. Giazotto and M. J. Martínez-Pérez, Nature 492, 401 (2012).
[4] F. Giazotto, M. J. Martínez-Pérez, and P. Solinas, Phys. Rev B 88, 094506
(2013).
[5] M. J. Martínez-Pérez and F. Giazotto, Nat. Commun. 5, 3579 (2014).
[6] A. Fornieri, C. Blanc, R. Bosisio, S. D'Ambrosio, and F. Giazotto, Nat. Nanotechnol. 11, 258 (2016).
[7] M. J. Martínez-Pérez and F. Giazotto, Appl. Phys. Lett. 102, 182602 (2013).
[8] F. Giazotto and F. S. Bergeret, Appl. Phys. Lett. 103, 242602 (2013).
[9] M. J. Martínez-Pérez, A. Fornieri, and F. Giazotto, , Nat. Nanotechnol. 10, 303 (2015).
Speaker: Prof. Francesco Giazotto (Scuola Normale Superiore)
• 16:45
Observation of dynamical Lee-Yang zeros 45m
Lee-Yang zeros are points in the complex plane of an external field where the partition function vanishes and the free energy diverges. In the thermodynamic limit, the Lee-Yang zeros approach the real value of the field for which a phase transition occurs. Lee-Yang zeros have been investigated theoretically, but experimental observations of Lee-Yang zeros remain scarce. Here, I describe our method for measuring Lee-Yang zeros and demonstrate how dynamical Lee-Yang zeros can be observed from the real-time detection of Andreev transitions across two tunneling barriers. The position of the Lee-Yang zeros has implications for the large-deviation statistics as I show. I conclude by identifying possible avenues for further developments.
Speaker: Prof. Christian Flindt (Aalto)
• 17:30
Quantum Jump Method with a Finite Environment 30m
Measurement of work done on a driven open quantum system remains a major challenge in quantum thermodynamics. A calorimetric detection method has been proposed by J. Pekola and collaborators [1] as a feasible experimental scheme to measure work and fluctuation relations in open quantum systems. However, the detection requires a finite size for the environment, which influences the system dynamics. This process cannot be modeled with the standard stochastic approaches. We develop a quantum jump model suitable for systems coupled to a finite-size environment and discuss its application to work measurement and fluctuation relations [2].
1. J. P. Pekola, P. Solinas, A. Shnirman, and D. V. Averin, New Journal of Physics 15, 115006 (2013).
2. S. Suomela, A. Kutvonen, and T. Ala-Nissila, to appear in Phys. Rev. E (2016).
Speaker: Prof. Tapio Ala-Nissila (Aalto)
• Saturday, 28 May
• 09:00 12:00
Saturday morning
• 09:00
Quantum Annealing and the Glass Problem 45m
Speaker: Prof. Jorge Kurchan (ENS)
• 09:45
Heat flux and information backflow in cold condensed matter systems 30m
We examine non-Markovian effects in an open quantum system from the point of view of information flow. To this end, we consider the spin-boson model with a cold reservoir, accounting for the exact time-dependent correlations between the system and the bath to study the exchange of information and heat. We use an information theoretic measure of the relevant memory effects and demonstrate that the information backflow from the reservoir to the system does not necessarily correlate with the backflow of heat. We also examine the influence of temperature and coupling strength on the loss and gain of information between the system and the bath. Finally, we discuss how additional driving changes the backflow of information, giving rise to potential applications in reservoir engineering.
Speaker: Dr Rebecca Schmidt (Aalto)
• 10:15
break 30m
• 10:45
Quantum trajectories and hindsight quantum states 45m
The state of a quantum system is described by a wavefunction evolving in time according to the Schroedinger equation. If a measurement is carried out on the system, its wave function collapses, i.e., it changes according to the random outcome of the measurement. During a sequence of measurements on a single system, its quantum state thus follows a stochastic trajectory composed of the normal quantum mechanical time evolution interrupted by collapses at each measurement. The resulting state of the system, at any time, successfully predicts the probabilities and mean values for the measurement of physical observables. In this talk we ask whether the sequence of measurements also adds to our knowledge about the state of the system at earlier times during the experiment. I shall show how such “hindsight” knowledge can be formally defined in quantum mechanics and how we can represent it via a time evolving (past) state, which at any time depends on both earlier and later measurement outcomes. I will show applications of this theory to experiments on atoms and superconducting qubits, and I will discuss how the concept and formalism of hindsight quantum states relate to questions of more foundational character.
Speaker: Prof. Klaus Mølmer (Aarhus)
• 11:30
Photonic Maxwell's Demon 30m
I will present a photonics experiment that can be understood as an example of Maxwell’s demon. In this experiment we showed that a measurement at the few-photons level performed on intense thermal light modes allows, by employing an operation conditional on measurement outcomes, the creation of an intensity unbalance, which we used to extract measurable work into an electric circuit. In order to interpret the experiment from a thermodynamic stand-point, we derived an equality relating work extraction to information acquired by measurement, which is to our knowledge novel. We obtained a bound on extractable work using this relation and compared it with experimental results. Our work puts forward photonics systems as a platform for experiments related to information in thermodynamics. In future work we aim to include the effects of quantum correlations in similar setups.
Speaker: Mr Mihai-Dorian Vidrighin (Oxford)