Haut PDF Driven-Dissipative Quantum Many-Body Systems

Driven-Dissipative Quantum Many-Body Systems

Driven-Dissipative Quantum Many-Body Systems

tems in presence of both driving and dissipation mechanisms represent natural platforms to understand and explore such dynamical phases. A well know example is provided by exciton-polariton condensates where superfluidity has an order parameter oscillating in time [ 30 , 31 , 70 , 122 ]. Yet the oscillating condensate is successfully described by semi- classical theories such as driven-dissipative Gross-Pitaevski equations that are valid in the regime of weak interactions. More recently the attention has shifted toward strongly correlated quantum lattice models with drive and dissipation, where several works have re- vealed the existence of limit cycles, i.e. non-stationary solutions of the quantum dynamics for a macroscopic order parameter, at least at the mean field level [ 16 , 17 , 20 , 93 , 187 – 189 ]. In this chapter we focus on a paradigmatic model of driven-dissipative interacting bosons on a lattice, which is directly relevant for the upcoming generation of circuit QED arrays experiments [ 61 , 62 , 86 ]. We argue that a dynamical susceptibility of such an open quantum many body system, which in thermal equilibrium is finite and small since non-zero frequency modes are typically damped by interactions, can display a genuine singularity at finite frequency, as a result of strong interactions and non-equilibrium effects. The critical frequency is non-trivial and set by a competition of interactions with drive and dissipation. Eventually, the system undergoes a dynamical phase transition where the order parameter emerges with a finite oscillation frequency and in the broken symmetry phase oscillates in time without damping, thus breaking the continuous time-translational symmetry. This stationary-state instability is controlled by both dissipative and coherent couplings, in particular by the ratio between hopping and local interaction, thus providing the strongly correlated analogue of weak coupling non-equilibrium bosons condensation.
En savoir plus

157 En savoir plus

Non-equilibrium dynamics of many body quantum systems

Non-equilibrium dynamics of many body quantum systems

In Chapter I we introduce the class of Spin-Boson models and focus in particular on the Rabi model, the ohmic spinboson model, and their lattice versions. The Rabi model considers a two-level system coupled to a quantized harmonic oscillator and de- scribes the simplest interaction between matter and light. Its lattice version describing a set of interacting light-matter systems opens the door to many-body physics with light. The ohmic spinboson model was first introduced to describe dissipative effects on a two-level system. In this description dissipation is modelled by a bath of quantized harmonic oscillators, and many-body effects of the bath notably induce a dissipa- tive quantum phase transition at large spin-bath coupling (see “Many-Body Quantum Electrodynamics Networks: Non-Equilibrium Condensed Matter Physics with Light”). In Chapter II, we derive a Stochastic Schr¨odinger Equation (SSE) describing the time evolution of the spin-reduced density matrix for Spin-boson problems. We test this framework and recover known results for the dynamics of the Rabi model (see “Quantum dynamics of the driven and dissipative Rabi model”) and the ohmic spinbo- son model. We also compare the SSE approach to other known methods and present the limitations related to the SSE.
En savoir plus

174 En savoir plus

A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems

A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems

Among our models, the most tractable is certainly the case of non-interacting fermions (strictly speaking, fermionic lattice systems are not covered here, but this could easily be remedied). It is therefore surprising that the phenomenon of ’localization in energy’ has barely been rigorously studied in the absence of interaction, i.e. for the one-particle case. In [12], localization was proved for periodically kicked operators. The authors of [37] considered the disordered Anderson model with a local time-periodic perturbation and proved the stability of localization. In [6], the same is achieved for a quasi-periodic perturbation, which can be viewed as the case of multiple frequency dimensions. Very recently, [15] considered the problem from a very similar point of view as in the present paper: [15] proves stability of Anderson localization with a periodic driving term, provided that the driving frequency is not too small. High-frequency asymptotics (instead of strict localization) in periodically driven quantum systems have been investigated in [16, 34, 39] by techniques similar to ours, but not applicable to the many-body problem.
En savoir plus

21 En savoir plus

Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems

Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems

mentally observed in a nearly integrable one-dimensional Bose gas 10 . In this paper, we establish some general properties of dynamics of periodically driven many-body systems (Floquet systems). Periodic driving in quantum systems has recently attracted much theoretical and experimental attention, because, amongst many applications, it pro- vides a tool for inducing effective magnetic fields, and for modifying topological properties of Bloch bands 11 – 14 . Indeed, since periodic driving is naturally realized in cold atomic systems by applying electromagnetic fields, topologically non-trivial Bloch bands (Floquet topologi- cal insulators) in non-interacting systems have been ob- served experimentally 15 – 17 . However, since periodic driv- ing breaks energy conservation, driven ergodic (many- body) systems are expected to heat up, eventually evolv- ing into a featureless, infinite-temperature state 18 – 21 . Thus, many-body effects are expected to generally make such Floquet systems unstable. Below, we derive gen- eral bounds for energy absorption rates in periodically driven many-body systems, which can be applied for in- stance to understand the lifetimes of Floquet topological insulators.
En savoir plus

10 En savoir plus

Driven dissipative dynamics and topology of quantum impurity systems

Driven dissipative dynamics and topology of quantum impurity systems

An environment can also serve for bath (or dissipation) engineering. We have illustrated this point by studying Kondo physics of light in Josephson circuits in the microwave limit, emergent Kondo physics in quantum RC circuits, multi-channel Kondo fixed points in topological Josephson junctions with Majorana fermions, and hybrid systems comprising a cQED environment coupled to a biased mesoscopic system. A dissipative environment engenders fluctuations and disorder in time; we have analyzed this aspect by building connections between Kondo and Quantum Brownian motion physics. These quantum impurity systems can also be useful as sensors of quantum many-body phenomena. We have illustrated this concept in ladder systems where the Rabi dynamics of a spin-1 /2 can probe the Mott-Superfluid transition. We have also studied the relaxation of particle densities and currents, in the language of spin-boson systems. Studying the fast dynamics in quantum materials has also attracted some attention recently, and our work could stimulate new frontiers.
En savoir plus

40 En savoir plus

Many-Body Localization in Periodically Driven Systems

Many-Body Localization in Periodically Driven Systems

Another implication of our results is that MBL does not rely on global conservation laws. Further, MBL phase is robust under sufficiently weak periodic driving, and there exists a finite driving threshold above which transport is restored, and the system ultimately delo- calizes. This may serve as an experimental signature of the many-body localization. An interesting subject for future research, relevant for experiments in disordered solid-state systems, is to study periodically driven MBL system weakly coupled to a thermal bath (we note that spectral properties of a static MBL system coupled to a bath were recently considered in Refs. [ 45 , 46 ]).
En savoir plus

7 En savoir plus

Out-Of-Equilibrium Dynamics and Locality in Long-Range Many-Body Quantum Systems

Out-Of-Equilibrium Dynamics and Locality in Long-Range Many-Body Quantum Systems

is sufficiently large. For the specific case of the Ising model, the operators γ k † γ k have been found to respect these conditions in [ 187 ]. The relaxation of different integrable models to the GGE has been tested explicitly in many different models as: Luttinger Liquids [ 189 , 190 ], free bosonic theories [ 191 , 192 ], hardcore bosons [ 187 ], Lieb-Lininger model [ 193 , 194 ], spin models [ 195 , 196 , 197 , 198 ] and Hubbard-like models [ 199 , 200 ]. The previous discussion is more an argument than a real theorem, even if thermalization has been found in some classes of models, a general theorem that states how different systems thermalize is still missing. Moreover, the exploration of long-time dynamics of many-body interacting quantum systems is, from the numerical point of view, extremely challenging. The possibility to simulate different Hamiltonians in experimental cold atomic gases plays then a key role in the exploration of the thermalization problem in such systems. As we said in Sec. 1.3 , cold atomic gases can be used to engineer different Hamiltonians and to drive them out of equilibrium. Moreover it is also possible to constraint systems in reduced dimensionality, as one or two dimensional geometries. Integrability is in fact an extremely delicate characteristic of the system, a fine tuning of all parameters of the Hamiltonian is needed to observe it. Extra terms in the Hamiltonian drive the system away from integrability and produce drastically different results. In classical physics the role of perturbations in an integrable theory is well understood using the KAM theory [ 3 ]. At the quantum level, however, this is not the case. Even small perturbations produce pre-thermalisation plateau [ 201 , 148 , 202 ] described by the GGE before that real thermalization occurs. Anyway, it is still not known how to define “small” and “large” in the context of perturbation around the integrable case.
En savoir plus

182 En savoir plus

Derivation of the two-dimensional nonlinear Schrodinger equation from many body quantum dynamics

Derivation of the two-dimensional nonlinear Schrodinger equation from many body quantum dynamics

Also in the-two dimensional problem discussed in the present paper, the correlations among the particles do not affect the macroscopic dynamics of the system (this explains why the coupling constant in front of the nonlinearity in (1.6) is just the integral of the potential). On the contrary, the correlation structure would be very important in the study of two-dimensional systems in the Gross-Pitaevskii scaling limit (where the scattering length of the interaction potential is exponentially small in the number of particles). In [23], Lieb, Seiringer, and Yngvason proved that, in this limit, the ground state energy per particle can be obtained by the minimization of the so called Gross-Pitaevskii energy functional. In [22], it was then shown by Lieb and Seiringer that the ground state vector, in the Gross-Pitaevskii limit, exhibits complete Bose Einstein condensation. In order to prove these two results, it was very important to identify the short scale correlation structure in the ground state wave function (the energy of factorized wave functions, with absolutely no correlations, is too large by a factor of N ). Unfortunately, we are not yet able to study the dynamics of Bose-Einstein condensates in the two-dimensional Gross- Pitaevskii scaling limit; nevertheless, since the infinite hierarchy which is expected to describe the time-evolution of the limiting densities {γ ∞,t (k) } k≥1 is still given by (2.9) (with a different coupling
En savoir plus

30 En savoir plus

Time Evolution of Many-Body Localized Systems with the Flow Equation Approach

Time Evolution of Many-Body Localized Systems with the Flow Equation Approach

(c † i c i+1 + hc) (1) with n i = c † i c i , where the on-site random field is drawn from a box distribution h i ∈ [−W, W ] and we set J = 1/2 as our unit of energy, to map exactly on the XXZ spin chain after Jordan-Wigner. Notice that FEs are a rather general and flexible approach which can be applied to other quantum disordered problems (see discussion for future applications). The basic idea of the FE approach is to iteratively diagonalize the Hamiltonian of the sys- tem by a CUT U (l) parametrized by a scale l and gen- erated by an anti-Hermitian operator η(l), such that U (l) = T l exp R η(l)dl  . The flow of any operator O(l)
En savoir plus

12 En savoir plus

Stochastic dissipative quantum spin chains (I) : Quantum fluctuating discrete hydrodynamics

Stochastic dissipative quantum spin chains (I) : Quantum fluctuating discrete hydrodynamics

Although we elaborated on the basic principles underlying the construction, we mainly concentrated on analysing the stochastic Heisenberg XXZ spin chain. Of course many ques- tions remain to be studied –transport, finite size systems with or without boundary injection, boundary effects, robustness to perturbations, etc (see ref.[28]). We dealt with the effective theory at large friction –but studying the sub-leading contributions could also be interest- ing as they generate a non-linear diffusion constant [29]. In this limit the effective quantum stochastic dynamics that we identified are natural quantizations of the fluctuating discrete hydrodynamic equations. They could now be directly taken as starting points for modelling quantum diffusive transports and their fluctuations, but the detour we took through the large friction limit justified their precise structures –and part of them, say the dressing of the hop- ping operators in the case of the XXZ spin chain, would had been difficult to guess without this detour. It is interesting to notice that stochasticity within conformal field theory has recently been considered in [13].
En savoir plus

31 En savoir plus

One particle equations for many particle quantum systems : the MCTHDF method

One particle equations for many particle quantum systems : the MCTHDF method

2 The MCTDHF ansatz As remarked above convenient approximations for a system of N interacting Fermions should not rely on a mean field hypothesis. N may be large, but a N → ∞ mean field limit in the weak coupling scaling does in general not correspond to the physics. The TDHF method also has the important disad- vantage that by definition it cannot catch ”correlations”, a crucial concept for N particle quantum systems (see e.g. [26, 27]). However, by approximating Ψ by linear combinations of Slater determinants, an approximation hierarchy called Multiconfiguration time dependent Hartree Fock (MCTDHF) is obtained that allows for very precise and numerically tractable models of correlated few body systems (see e.g. [11, 43]). The MCTDHF ansatz involves a finite number
En savoir plus

20 En savoir plus

A note on 2D focusing many-boson systems

A note on 2D focusing many-boson systems

MATHIEU LEWIN, PHAN TH ` ANH NAM, AND NICOLAS ROUGERIE Abstract. We consider a 2D quantum system of N bosons in a trapping potential |x| s , interacting via a pair potential of the form N 2β−1 w(N β x). We show that for all 0 < β < (s + 1)/(s + 2), the leading order behavior of ground states of the many-body system is described in the large N limit by the corresponding cubic nonlinear Schr¨ odinger energy functional. Our result covers the focusing case (w < 0) where even the stability of the many-body system is not obvious. This answers an open question mentioned by X. Chen and J. Holmer for harmonic traps (s = 2). Together with the BBGKY hierarchy approach used by these authors, our result implies the convergence of the many-body quantum dynamics to the focusing NLS equation with harmonic trap for all 0 < β < 3/4.
En savoir plus

15 En savoir plus

Absence of many-body mobility edges

Absence of many-body mobility edges

PACS numbers: 05.30.Rt, 72.15.Rn, 72.20.Ee I. INTRODUCTION It is now almost mathematically proven that many- body localization, i.e., the absence of long-range trans- port in a thermodynamic many-body system, occurs in certain one-dimensional quantum lattice models at any energy density if sufficiently strong quenched disorder is present [1]. In this case, many-body localization (MBL) comes along with a complete set of conserved quasi- local quantities [2–4]. However, it remains less clear whether the originally predicted localization transition at finite temperature [5, 6] exists as a genuine dynam- ical phase transition defining a sharp many-body mo- bility edge in energy density. Even though several nu- merical investigations in small one-dimensional (1D) sys- tems have reported such mobility edges [7–9], studies in larger systems did not find similar evidence [10, 11] and, moreover, linked-cluster analysis [12] of the numer- ical data hint that the extent of the localized phase has been vastly overestimated. Furthermore, recent theoret- ical considerations [4, 13–16] have raised doubts about non-perturbative effects which might reduce the putative transition to a crossover. A related open issue concerns the many-body analog of Mott’s argument, which forbids the coexistence of localized and delocalized states at the same energy in single-particle problems.
En savoir plus

16 En savoir plus

Delocalized Glassy Dynamics and Many Body Localization

Delocalized Glassy Dynamics and Many Body Localization

Understanding the inter-play of quenched disorder, in- teractions and quantum fluctuations has been a central theme of hard condensed matter for many years. Activ- ity on this topic boomed recently, in particular after that Basko, Aleiner and Altshuler (BAA) showed by using the self-consistent Born approximation that interacting and isolated quantum systems can fail to thermalize due to Anderson localization in Fock space [1]. This phe- nomenon, called Many Body Localization (MBL), repre- sents a new kind of ergodicity breaking transition, which is purely dynamical—indeed it can take place even at infi- nite temperature by increasing the amount of disorder— and which results from the interplay of disorder, interac- tions and quantum fluctuations [2, 3]. One of the most surprising results is that even the delocalized phase is unusual in a wide range of parameters already before the MBL transition. In fact both in numerical simulations [4– 8] and in experiments [9–11] it was found that transport appears to be sub-diffusive and that out-of-equilibrium relaxation toward thermal equilibrium is slow and power- law-like with exponents that gradually approach zero at the transition. Several works explained this behavior in terms of Griffiths regions, i.e., rare inclusions of the lo- calised phase which impede transport and relaxation [12– 15]. However, also quasi-periodic 1d and disordered 2d systems, in which Griffiths effects should be absent or milder [14, 15], do display analogous unusual transport and relaxation [10, 11, 16, 17]. It is therefore important to look for other explanations that might hold beyond the particular case of 1d disordered systems. Moreover, it is interesting to complement the real space Griffiths perspective to one directly based on quantum dynamics in Fock-space. These are the aims of our work.
En savoir plus

7 En savoir plus

Electron-phonon coupling and charge-transfer excitations in organic systems from many-body perturbation theory

Electron-phonon coupling and charge-transfer excitations in organic systems from many-body perturbation theory

Laboratoire de Simulation Atomistique (L Sim), SP2M, INAC, CEA-UJF 17 Av. des Martyrs, 38054 Grenoble, France. Even though organic systems offer an extremely large flexibility in terms of available molecules and architec- tures, the rather low quantum efficiency (a few per- cent), as compared to standard silicon-based solar cells, and the problems of stability under UV radiations, are serious limitations that need to be addressed. It has been shown however that significant gains [5,6] can be achieved by tuning the absorption spectrum, band gap and band offsets of the active molecules/polymers in standard donor/acceptor hetero-structure cells [7–9]. Using computer quantum simulations to predict such spectroscopic parameters for actual size molecules or polymers would therefore be of much interest.
En savoir plus

12 En savoir plus

Strongly driven quantum Josephson circuits

Strongly driven quantum Josephson circuits

In the past, atomic systems, optical systems or trapped ions systems have been investigated as a basis to implement such quantum machines. However, since the first demonstration of a quantum superconducting bit, more than twenty years ago [5, 6], the domain of mesoscopic artificial atoms built out of superconducting quantum circuits became one of the most promising physical system to implement quantum machines. Such circuits can be used to create resonators which store individual microwave photons as well as superconducting quantum bits. All of these circuit elements are intrinsically quantum mechanical, with quantized energy levels with spacing much greater than the energy associated with the temperature (for cryogenic temperatures which are achievable in the laboratory) and in order to properly predict their properties, both the current and voltages should be represented by non-commuting operators. The coherence time of these circuits have improved rapidly and steadily over a few orders of magnitude, now reaching a few milliseconds for the best systems [7, 8, 9, 10, 11]. Contrary to the atomic physics based systems, such superconducting circuits provide greater flexibility in the range of exploitable parameters and in the complexity of the Hamiltonian they can implement. This flexibility let us explore a whole new realm of operating regimes. Moreover, the microwave signals, contrary to the optical ones, are very well controlled with commercial electronic equipment developed for radio-frequency engineering. The nanofabrication processes required to fabricate such quantum superconducting circuits are more and more controlled, so that it becomes possible to fabricate multiple complex systems in parallel, leading to the hope that it will soon be possible to scale such quantum processors with large numbers of qubits and leading to the recent development of many commercial interests (from Google, IBM, Intel or Rigetti Computing).
En savoir plus

108 En savoir plus

Flow towards diagonalization for Many-Body-Localization models : adaptation of the Toda matrix differential flow to random quantum spin chains

Flow towards diagonalization for Many-Body-Localization models : adaptation of the Toda matrix differential flow to random quantum spin chains

The iterative methods to diagonalize matrices and many-body Hamiltonians can be reformulated as flows of Hamiltonians towards diagonalization driven by unitary transformations that preserve the spectrum. After a comparative overview of the various types of discrete flows (Jacobi, QR- algorithm) and differential flows (Toda, Wegner, White) that have been introduced in the past, we focus on the random XXZ chain with random fields in order to determine the best closed flow within a given subspace of running Hamiltonians. For the special case of the free-fermion random XX chain with random fields, the flow coincides with the Toda differential flow for tridiagonal matrices which is related to the classical integrable Toda chain and which can be seen as the continuous analog of the discrete QR-algorithm. For the random XXZ chain with random fields that displays a Many- Body-Localization transition, the present differential flow should be an interesting alternative to compare with the discrete flow that has been proposed recently to study the Many-Body-Localization properties in a model of interacting fermions (L. Rademaker and M. Ortuno, Phys. Rev. Lett. 116, 010404 (2016)).
En savoir plus

25 En savoir plus

Quantum Quasi-Monte Carlo Technique for Many-Body Perturbative Expansions

Quantum Quasi-Monte Carlo Technique for Many-Body Perturbative Expansions

The exponential complexity of quantum many-body systems is at the heart of many remarkable phenomena. Advances in correlated materials and recently developed synthetic quantum systems – e.g. atomic gases [ 1 ], trapped ions [ 2 ], and nanoelectronic devices [ 3 – 6 ] – have allowed many-body states to be characterized and controlled with unprecedented precision. The latest of these systems, quantum computing chips, are highly engineered out-of- equilibrium many-body systems, where the interacting dynamics performs computational tasks [ 7 ]. However, our understanding of these many-body systems is limited by their intrinsic complexity. While uncontrolled approxi- mations can give insight into possible behaviors, there is a growing effort to develop controlled, high-precision methods [ 8 ], especially ones that apply far from equilib- rium [ 9 – 11 ]. These allow us to make quantitative pre- dictions about the physics of many-body systems and to uncover qualitatively new effects at strong coupling.
En savoir plus

17 En savoir plus

Microscopic approaches for nuclear Many-Body dynamics: applications to nuclear reactions

Microscopic approaches for nuclear Many-Body dynamics: applications to nuclear reactions

These lecture notes are addressed to PhD student and/or researchers who want a general overview of microscopic approaches based on mean-field and applied to nuclear dynamics. Our goal is to provide a good description of low energy heavy-ion collisions. We present both formal aspects and practical applications of the time-dependent Hartree-Fock (TDHF) theory. The TDHF approach gives a mean field dynamics of the system under the assumption that particles evolve independently in their self-consistent average field. As an example, we study the fusion of both spherical and deformed nuclei with TDHF. We also focus on nucleon transfer which may occur between nuclei below the barrier. These studies allow us to specify the range of applications of TDHF in one hand, and, on the other hand, its intrinsic limitations: absence of tunneling below the Coulomb barrier, missing dissipative effects and/or quantum fluctuations. Time-dependent mean-field theories should be improved to properly account for these effects. Several approaches, generically named ”beyond TDHF” are presented which account for instance for pairing and/or direct nucleon-nucleon collisions. Finally we discuss recent progresses in exact ab-initio methods based on the stochastic mean-field concept.
En savoir plus

56 En savoir plus

Projected Bogoliubov Many-Body Perturbation Theory : Overcoming formal and technical challenges

Projected Bogoliubov Many-Body Perturbation Theory : Overcoming formal and technical challenges

in the context of MBPT by employing NCSM reference states [ 22 ]. A second option of present interest is to exploit the concept of spontaneous symmetry breaking, breaking e.g. U (1) symmetry associated to the particle number conservation in order to capture the superfluid character of singly-open-shell nuclei. Doubly-open-shell nuclei can be addressed as well via the breaking of SU (2) symmetry associated with the angular-momentum conservation, allowing for nuclei to deform. Breaking U (1) symmetry allows one to deal with Cooper pair’s instability and capture the dominant effect of the infrared source of non- perturbativeness already at the level of the reference state. Via the use of a more general Bogoliubov vacuum, the degeneracy of an open-shell Slater determinant with respect to particle-hole excitations is lifted and commuted into a degeneracy with respect to symmetry transformations of the symmetry-broken group (U (1) in this case). As a consequence, the ill-defined (i.e. singular) expansion of exact quantities around a Slater determinant is replaced by a well-behaved one around a Bogoliubov state. Symmetry breaking has been used for decades by the EDF community [ 41 – 44 ], i.e. at the mean field level. In the last ten years, novel ab initio many-body methods have been developed on top of symmetry-broken reference states, e.g. the Gorkov SCGF (GSCGF) framework [ 45 – 47 ], the Bogoliubov CC (BCC) formalism [ 48 , 49 ], the Bogoliubov MBPT (BMBPT) [ 50 , 51 ] and even the Bogoliubov CI (BCI) [ 52 , 53 ], the last one not being an expansion method. A difficulty encountered by these methods is that the symmetry breaking cannot actually occur in finite quantum systems and results of many-body calculations carry a contamination associated with contributions of non-targeted particle numbers, i.e. of several irreducible representations of the broken symmetry group.
En savoir plus

221 En savoir plus

Show all 10000 documents...