Javier Prior

Efficient Simulation of Strong System-Environment Interactions

Multicomponent quantum systems in strong interaction with their environment are receiving increasing attention due to their importance in a variety of contexts, ranging from solid state quantum information processing to the quantum dynamics of biomolecular aggregates. Unfortunately, these systems are difficult to simulate as the system-bath interactions cannot be treated perturbatively and standard approaches are invalid or inefficient. Here we combine the time-dependent density matrix renormalization group with techniques from the theory of orthogonal polynomials to provide an efficient method for simulating open quantum systems, including spin-boson models and their generalizations to multicomponent systems.

Vibronic origin of long-lived coherence in an artificial molecular light harvester

Natural and artificial light-harvesting processes have recently gained new interest. Signatures of long-lasting coherence in spectroscopic signals of biological systems have been repeatedly observed, albeit their origin is a matter of ongoing debate, as it is unclear how the loss of coherence due to interaction with the noisy environments in such systems is averted. Here we report experimental and theoretical verification of coherent exciton–vibrational (vibronic) coupling as the origin of long-lasting coherence in an artificial light harvester, a molecular J-aggregate. In this macroscopically aligned tubular system, polarization-controlled 2D spectroscopy delivers an uncongested and specific optical response as an ideal foundation for an in-depth theoretical description. We derive analytical expressions that show under which general conditions vibronic coupling leads to prolonged excited-state coherence.

Generalized polaron ansatz for the ground state of the sub-Ohmic spin-boson model: an analytic theory of the localization transition.

The sub-ohmic spin-boson model is known to possess a novel qu antum phase transition at zero temperature between a localised and delocalised phase. We present here a n analytical theory based on a variational ansatz for the ground state, which describes a continuous localiza tion transition with mean-field exponents for 0 < s < 0.5. Our results for the critical properties show good quantiti ative agreement with previous numerical results, and we present a detailed description of all the spin observa bles as the system passes through the transition. Analysing the ansatz itself, we give an intuitive microscop i description of the transition in terms of the changing correlations between the system and bath, and show that it is always accompanied by a divergence of the lowfrequency boson occupations. The possible relevance of thi s divergence for some numerical approaches to this problem is discussed and illustrated by looking at the groun d state obtained using density matrix renormalisation group methods.

Exact matrix product solutions in the Heisenberg picture of an open quantum spin chain

In recent work Hartmann et al [Phys. Rev. Lett. 102, 057202 (2009)] demonstrated that the classical simulation of the dynamics of open 1D quantum systems with matrix product algorithms can often be dramatically improved by performing time evolution in the Heisenberg picture. For a closed system this was exemplified by an exact matrix product operator solution of the time-evolved creation operator of a quadratic fermi chain with a matrix dimension of just two. In this work we show that this exact solution can be significantly generalized to include the case of an open quadratic fermi chain subjected to master equation evolution with Lindblad operators that are linear in the fermionic operators. Remarkably even in this open system the time-evolution of operators continues to be described by matrix product operators with the same fixed dimension as that required by the solution of a coherent quadratic fermi chain for all times. Through the use of matrix product algorithms the dynamical behaviour of operators in this non-equilibrium open quantum system can be computed with a cost that is linear in the system size. We present some simple numerical examples which highlight how useful this might be for the more detailed study of open system dynamics. Given that Heisenberg picture simulations have been demonstrated to offer significant accuracy improvements for other open systems that are not exactly solvable our work also provides further insight into how and why this advantage arises.

Density matrix renormalization group in the Heisenberg picture

In some cases the state of a quantum system with a large number of subsystems can be approximated efficiently by the density-matrix renormalization group, which makes use of redundancies in the description of the state. Here we show that the achievable efficiency can be much better when performing density-matrix renormalization group calculations in the Heisenberg picture, as only the observable of interest but not the entire state is considered. In some nontrivial cases, this approach can even be exact for finite bond dimensions.

Coherence-assisted single-shot cooling by quantum absorption refrigerators

The extension of thermodynamics into the quantum regime has received much attention in recent years. A primary objective of current research is to find thermodynamic tasks which can be enhanced by quantum mechanical effects. With this goal in mind, we explore the finite-time dynamics of absorption refrigerators composed of three quantum bits (qubits). The aim of this finite-time cooling is to reach low temperatures as fast as possible and subsequently extract the cold particle to exploit it for information processing purposes. We show that the coherent oscillations inherent to quantum dynamics can be harnessed to reach temperatures that are colder than the steady state in orders of magnitude less time, thereby providing a fast source of low-entropy qubits. This effect demonstrates that quantum thermal machines can surpass classical ones, reminiscent of quantum advantages in other fields, and is applicable to a broad range of technologically important scenarios.

Computation of Two-Dimensional Spectra Assisted by Compressed Sampling.

The computation of scientific data can be very time-consuming, even if they are ultimately determined by a small number of parameters. The principle of compressed sampling suggests that for typical data we can achieve a considerable decrease in the computation time by avoiding the need to sample the full data set. We demonstrate the usefulness of this approach at the hand of two-dimensional (2-D) spectra in the context of ultrafast nonlinear spectroscopy of biological systems where numerical calculations are highly challenging due to the considerable computational effort involved in obtaining individual data points.

Wavelet analysis of molecular dynamics: Efficient extraction of time-frequency information in ultrafast optical processes

Javier Prior, Enrique Castro, Alex W. Chin, Javier Almeida, Susana F. Huelga, and Martin B. Plenio Departamento de F́ısica Aplicada, Universidad Politécnica de Cartagena, Cartagena 30202, Spain Theory of Condensed Matter Group, University of Cambridge, J J Thomson Avenue, Cambridge, CB3 0HE, United Kingdom Institut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm, D-89069 Ulm, Germany (Dated: May 11, 2014)

Realising a quantum absorption refrigerator with an atom-cavity system

An autonomous quantum thermal machine comprising a trapped atom or ion placed inside an optical cavity is proposed and analysed. Such a machine can operate as a heat engine whose working medium is the quantised atomic motion, or as an absorption refrigerator which cools without any work input. Focusing on the refrigerator mode, we predict that it is possible with state-of-the-art technology to cool a trapped ion almost to its motional ground state using a thermal light source such as sunlight. We nonetheless find that a laser or similar reference system is necessary to stabilise the cavity frequencies. Furthermore, we establish a direct and heretofore unacknowledged connection between the abstract theory of quantum absorption refrigerators and practical sideband cooling techniques. We also highlight and clarify some assumptions underlying several recent theoretical studies on self-contained quantum engines and refrigerators. Our work indicates that cavity quantum electrodynamics is a promising and versatile experimental platform for the study of autonomous thermal machines in the quantum domain.

Entanglement, tensor networks and black hole horizons

We elaborate on a previous proposal by Hartman and Maldacena on a tensor network which accounts for the scaling of the entanglement entropy in a system at a finite temperature. In this construction, the ordinary entanglement renormalization flow given by the class of tensor networks known as the Multi Scale Entanglement Renormalization Ansatz (MERA), is supplemented by an additional entanglement structure at the length scale fixed by the temperature. The network comprises two copies of a MERA circuit with a fixed number of layers and a pure matrix product state which joins both copies by entangling the infrared degrees of freedom of both MERA networks. The entanglement distribution within this bridge state defines reduced density operators on both sides which cause analogous effects to the presence of a black hole horizon when computing the entanglement entropy at finite temperature in the AdS/CFT correspondence. The entanglement and correlations during the thermalization process of a system after a quantum quench are also analyzed. To this end, a full tensor network representation of the action of local unitary operations on the bridge state is proposed. This amounts to a tensor network which grows in size by adding succesive layers of bridge states. Finally, we discuss on the holographic interpretation of the tensor network through a notion of distance within the network which emerges from its entanglement distribution.