The key objective of the project
is to explorequantum attractors, a class of time-periodic asymptotic states of open many-body quantum systems which are subjected to periodic modulations of their parameters
Motivation
I Many-body quantum systemsare at the center of active studies, both in theoretical and experimental corners. They started to prevail in the field of quantum nano-electromechanical systems(NEMS), quantum opto-mechanicsandsemiconductor matter-light systems;
I Macroscopic nature of experimental realizations of these systems makes their complete isolation from the environment impossible.
These system are open and their coherent quantum evolution is limited by finite timescales. It is important to understand the asymptotic regimes of these systems, out-shaped by the joint efforts ofdecoherence and the system internal quantum dynamics. This is a key tosustainable quantum devices;
I Periodic modulationscan be very helpful in this context. First, they can introduce an additional, “enforced”, coherence into an open system.
Second, they provide a way tosculpturedesirable asymptotic states of the system.
An example: Cavity-QED system
A photon driven quantum-dot cavity-QED system. A periodic train of identical photons enters into an optical cavity. The parameterg specifies the strength of the interaction between a two-level quantum dot and the photon field. When the period of the photon train is comparable with one of the characteristic timescales of the intra- cavity dynamics (lifetime of excitons, inverse Rabi splitting between exciton and photon modes, etc.), the dynamics becomes strongly non-equilibrium. The photoluminescence emission from the cavity provides a key-hole to take a look into the intra-cavity states.
Quantum attractors: what are they ?
They are essentially non-equilibrium states of open periodically-driven many-body quantum systems. These states are characterized by time- periodic density matrices to which systems ’relax’ in course of time.
I called them, therefore,quantum attractors.
Asingle-particle quantum attractor. I used a model withN= 300states only and the method of direct diagonalization (discussed on the next slide). It took200hours simulations on the standard six-core computational cluster.
Why is it challenging and has not been done already?
The existing results resolve states of simple open systems on the time scalestoo short to talk about quantum attractors.
A straightforward method to find a stationary asymptotic state is thecomplete diagonalizationof the superoperator, which governs the density matrix of the system. It isa tough computational problem already in case of a system of with a few hundred states (see the previous slide). The problem becomes even more dramatic when the system isperiodically modulated.
An alternative is a statistical sampling by usingthe method of “quantum jumps”. However, the temporal horizon of these stochastic simulations (even in the case oftime-independent systems) is severely limited by exponentially growing statistical fluctuations.
Two ways to compute quantum attractors
Two computational ways to find quantum attractors. (left) It can be obtained by the direct diagonalization of a super-operator, which accounts for both actions, of a time- dependent system Hamiltonian and the environment.This is a massive numerical task which is limited by the size of the quantum system and allows to handle systems with a few hundreds of states only.(right) The method of quantum jumps is an alternative to the brute-force diagonalization and allows to handle much larger quantum systems.This approach allows to avoid the diagonalization of huge matrices for the price of statistical sampling over astronomically large numbers of trajectories.
Theoretical problems related to quantum attractors
The objectives of the project are not limited by the applied and computational aspects. A complimentary goal is to answer some questions&issues recently arisen in the theoretical quantum community.
For example,
I Many-body localizationis a hot topic. Adrivingwas introduced very recently in this field to see what it could do to the localization. The question what thedecoherencecould do to it is even more intriguing;
I The Bose-Einstein condensation in quasiparticle systems(f. e., exciton- polariton ensembles), where the systems are not only open but the total number of particles in them is not conserved;
I Building of the theory of dissipative many-body quantum chaosand elucidation of its relations to the classical dissipative chaos (in the manner similar it has been done for theHamiltonian chaos).
Means
The realization of the project requires combinations of methods from three different fields, namely
I Floquet theory of periodically driven quantum systems;
I theory of open quantum systems;
I high-performance scientific computing.
Massive numerical experiments will demand new algorithms, which will be built up by using methods of parallel programming and newest high-performance computation technologies, such as a blend of general purpose graphics processing units (GPUs) with Xeon Phi processors.
The group
The group is planned to consist offive people (including myself).
I Two team members will be hired on the post-doc level. They need to have an expertise both in quantum and computational physics;
I One member is planned to be a professional programmer, with an expertise in the GPU computing. He/she will be hired on the level of the research officer;
I Finally,one person will be taken in as a PhD student. The project development will guide his/her studies.
In order to accomplish the goals of the project, we will need aGraphic Processing Unit (GPU) computational cluster with an inclusion of Xeon Phi proceesors. It will be assembled during the first months after the project starts. I estimate the related expenses ∼ W 70 - 80 millions.
Why at the IBS Center for Theoretical Physics of Complex Systems?
First of all, the project perfectly fits the key research lines and objectives of the Center:
Our center aims to take up the grand challenge and to create a world-class laboratory for the nonlinear classical and quantum dynamics of nano-structured systems, and to conduct cutting edge research on phenomena at theinterfaces of applied and computational theoretical condensed matter physics and optics. We aim to cross- fertilize research on ... ultracold atomic gases, .. many body localization, disorder against interactions, ... coherence anddecoherence, andquantum stochastic dynamics.
Next, I do believe that the project group and the Center willsymbiotically benefitfrom each other.
While the Center is going to be a one of the strongholds of theoretical nanoscience in the Republic of Korea, the group could serve as a computational “arm” of the institute.
