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Register a new userCorrespondence on Single-shot simulations of dynamic quantum many-body systems
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Comment on a letter to Nature Physics, where Sakmann and Kasevich claim to solve the many-body time dependent Schrodinger equation to simulate single experimental runs of interacting quantum systems.
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The single-particle density is the most basic quantity that can be calculated from a given many-body wave function. It provides the probability to find a particle at a given position when the average over many realizations of an experiment is taken. However, the outcome of single experimental shots of ultracold atom experiments is determined by the $N$-particle probability density. This difference can lead to surprising results. For example, independent Bose-Einstein condensates (BECs) with definite particle numbers form interference fringes even though no fringes would be expected based on the single-particle density [1-4]. By drawing random deviates from the $N$-particle probability density single experimental shots can be simulated from first principles [1, 3, 5]. However, obtaining expressions for the $N$-particle probability density of realistic time-dependent many-body systems has so far been elusive. Here, we show how single experimental shots of general ultracold bosonic systems can be simulated based on numerical solutions of the many-body Schrodinger equation. We show how full counting distributions of observables involving any number of particles can be obtained and how correlation functions of any order can be evaluated. As examples we show the appearance of interference fringes in interacting independent BECs, fluctuations in the collisions of strongly attractive BECs, the appearance of randomly fluctuating vortices in rotating systems and the center of mass fluctuations of attractive BECs in a harmonic trap. The method described is broadly applicable to bosonic many-body systems whose phenomenology is driven by information beyond what is typically available in low-order correlation functions.
We introduce a new approach for the robust control of quantum dynamics of strongly interacting many-body systems. Our approach involves the design of periodic global control pulse sequences to engineer desired target Hamiltonians that are robust against disorder, unwanted interactions and pulse imperfections. It utilizes a matrix representation of the Hamiltonian engineering protocol based on time-domain transformations of the Pauli spin operator along the quantization axis. This representation allows us to derive a concise set of algebraic conditions on the sequence matrix to engineer robust target Hamiltonians, enabling the simple yet systematic design of pulse sequences. We show that this approach provides an efficient framework to (i) treat any secular many-body Hamiltonian and engineer it into a desired form, (ii) target dominant disorder and interaction characteristics of a given system, (iii) achieve robustness against imperfections, (iv) provide optimal sequence length within given constraints, and (v) substantially accelerate numerical searches of pulse sequences. Using this systematic approach, we develop novel sets of pulse sequences for the protection of quantum coherence, optimal quantum sensing and quantum simulation. Finally, we experimentally demonstrate the robust operation of these sequences in a system with the most general interaction form.
Closed quantum many-body systems out of equilibrium pose several long-standing problems in physics. Recent years have seen a tremendous progress in approaching these questions, not least due to experiments with cold atoms and trapped ions in instances of quantum simulations. This article provides an overview on the progress in understanding dynamical equilibration and thermalisation of closed quantum many-body systems out of equilibrium due to quenches, ramps and periodic driving. It also addresses topics such as the eigenstate thermalisation hypothesis, typicality, transport, many-body localisation, universality near phase transitions, and prospects for quantum simulations.
Thermodynamics of quantum systems out-of-equilibrium is very important for the progress of quantum technologies, however, the effects of many body interactions and their interplay with temperature, different drives and dynamical regimes is still largely unknown. Here we present a systematic study of these interplays: we consider a variety of interaction (from non-interacting to strongly correlated) and dynamical (from sudden quench to quasi-adiabatic) regimes, and draw some general conclusions in relation to work extraction and entropy production. As treatment of many-body interacting systems is highly challenging, we introduce a simple approximation which includes, for the average quantum work, many-body interactions only via the initial state, while the dynamics is fully non-interacting. We demonstrate that this simple approximation is surprisingly good for estimating both the average quantum work and the related entropy variation, even when many-body correlations are significant.
Recently developed quantum algorithms suggest that in principle, quantum computers can solve problems such as simulation of physical systems more efficiently than classical computers. Much remains to be done to implement these conceptual ideas into actual quantum computers. As a small-scale demonstration of their capability, we simulate a simple many-fermion problem, the Fano-Anderson model, using liquid state Nuclear Magnetic Resonance (NMR). We carefully designed our experiment so that the resource requirement would scale up polynomially with the size of the quantum system to be simulated. The experimental results allow us to assess the limits of the degree of quantum control attained in these kinds of experiments. The simulation of other physical systems, with different particle statistics, is also discussed.
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