Quantum Reservoir Research Articles

Generation of two-mode entangled states by quantum reservoir engineering

A method for generating entangled cat states of two modes of a microwave cavity field is proposed. Entanglement results from the interaction of the field with a beam of atoms crossing the microwave resonator, giving rise to non-unitary dynamics of which the target entangled state is a fixed point. We analyse the robustness of the generated two-mode photonic ‘cat state’ against dephasing and losses by means of numerical simulation. This proposal is an instance of quantum reservoir engineering of photonic systems.

Coupled quantum oscillators within independent quantum reservoirs

This paper addresses the problem of open quantum systems. The energy of interaction of coupled dissipative systems is the main focus of the study. Quantum Langevin equations for two quantum coupling oscillators within independent heat baths of quantum oscillators are obtained using a model Hamiltonian and corresponding Heisenberg equations of motion. Analytical expressions for mean energy of coupled oscillators and their mean energy of interaction are derived and analyzed. Nonmonotonic dependence of the interaction energy versus a coupling constant is demonstrated and an explanation is suggested.

Quantum reservoir engineering and single qubit cooling

Abstract Stabilizing a quantum system in a desired state has important implications in quantum information science. In control engineering, stabilization is usually achieved by the use of feedback. The closed-loop control paradigm consists of measuring the system in a non-destructive manner, analyzing in real-time the measurement output to estimate the dynamical state and finally, calculating a feedback law to stabilize the desired state. However, the rather short dynamical time-scales of most quantum systems impose important limitations on the complexity of real-time output signal analysis and retroaction. An alternative control approach for quantum state stabilization, bypassing a real-time analysis of output signal, is called reservoir engineering. In this paper, we start with a general description of quantum reservoir engineering. We then apply this method to stabilize the ground state (lowest energy state) of a single two-level quantum system. Applying the averaging theorem and some simple Lyapunov techniques, we prove the convergence of our proposed scheme. This scheme has recently been successfully implemented on a superconducting qubit and has led to a fast and reliable reset protocol for these qubits.

Fermionic superoperators for zero-temperature nonlinear transport: Real-time perturbation theory and renormalization group for Anderson quantum dots

We study the transport through a strongly interacting Anderson quantum dot at zero-temperature using the real-time renormalization group (RT-RG) in the framework of a kinetic equation for the reduced density operator. We further develop the general finite temperature real-time transport formalism by introducing field superoperators that obey fermionic statistics. This direct second quantization in Liouville-Fock space strongly simplifies the construction of operators and superoperators which transform irreducibly under the Anderson-model symmetry transformations. The fermionic field superoperators naturally arise from the univalence (fermion-parity) superselection rule for the total system. Expressed in these field superoperators, the causal structure of the perturbation theory for the effective time-evolution superoperator-kernel becomes explicit. The causal structure also implies the existence of a fermion-parity protected eigenvector of the exact Liouvillian, explaining a recently reported result on adiabatic driving [Phys. Rev. B 85, 075301 (2012)] and generalizing it to arbitrary order in the tunnel coupling. Furthermore, in the WBL the causal representation exponentially reduces the number of diagrams for the time-evolution kernel. We perform a complete 2-loop RG analysis at finite voltage and magnetic field, while systematically accounting for the dependence on both the quantum dot and reservoir frequencies. Using the second quantization in Liouville-space and symmetry restrictions we obtain analytical RT-RG equations with an efficient numerical solution and we extensively study the model parameter space, excluding the Kondo regime. The incorporated renormalization effects result in an enhancement of the inelastic cotunneling peak. Moreover, we find a tunnel-induced non-linearity of the stability diagrams at finite voltage, both in the SET and ICT regime.

Stabilization of nonclassical states of one- and two-mode radiation fields by reservoir engineering

We analyze a quantum reservoir engineering method, originally introduced by [Sarlette et al. in Phys. Rev. Lett. 107, 010402 (2011) -- arXiv 1011.5057], for the stabilization of non-classical field states in high quality cavities. We generalize the method to the protection of mesoscopic entangled field states shared by two non-degenerate field modes. The reservoir is made up of a stream of atoms undergoing successive composite interactions with the cavity, each combining resonant with non-resonant parts. We get a detailed insight into the competition between the engineered reservoir and decoherence. We show that the operation is quite insensitive to experimental imperfections and that it could thus be implemented in the near future, either in the context of microwave Cavity Quantum Electrodynamics or in that of circuit-QED.

Stabilizing open quantum systems by Markovian reservoir engineering

We study open quantum systems whose evolution is governed by a master equation of Kossakowski-Gorini-Sudarshan-Lindblad type and give a characterization of the convex set of steady states of such systems based on the generalized Bloch representation. It is shown that an isolated steady state of the Bloch equation cannot be a center, i.e., that the existence of a unique steady state implies attractivity and global asymptotic stability. Necessary and sufficient conditions for the existence of a unique steady state are derived and applied to different physical models including two- and four-level atoms, (truncated) harmonic oscillators, composite and decomposable systems. It is shown how these criteria could be exploited in principle for quantum reservoir engineeing via coherent control and direct feedback to stabilize the system to a desired steady state. We also discuss the question of limit points of the dynamics. Despite the non-existence of isolated centers, open quantum systems can have nontrivial invariant sets. These invariant sets are center manifolds that arise when the Bloch superoperator has purely imaginary eigenvalues and are closely related to decoherence-free subspaces.

Engineering atomic quantum reservoirs for photons

We present protocols for creating entangled states of two modes of the electromagnetic field by using a beam of atoms crossing microwave resonators. The atoms are driven by a transverse, classical field and pump correlated photons into (i) two modes of a cavity and (ii) the modes of two distant cavities. The protocols are based on a stochastic dynamics, characterized by random arrival times of the atoms and by random interaction times between atoms and cavity modes. The resulting effective model yields a master equation, whose steady state is an entangled state of the cavity modes. In this respect, the atoms act like a quantum reservoir, pulling the cavity modes into an entangled, Einstein-Podolski-Rosen state, whose degree of entanglement is controlled by the intensity and the frequency of the transverse field. This scheme is robust against stochastic fluctuations in the atomic beam, and it does not require atomic detection nor velocity selection.

Energy and Oil - A Personal Journey

Academia.edu@TWA Nansen G. Saleri reflects on his career in the oil and gas industry. I entered the world of energy in 1974—many moons ago by any account—with Standard Oil of California (today's Chevron). All my degrees were in chemical engineering, so it made sense to be employed by the refining end of the business. Chevron offered me a choice of two research positions: one in their downstream research facility near San Francisco and the other with the upstream counterpart in southern California. The latter became my "accidental" selection per my wife Marina's fear of San Francisco earthquakes. That choice captures my life. Some of the best things in our lives happen due to luck or accidents. I have no way of knowing where I would be today if my wife's field of knowledge about California's tectonics pushed my decision (and hers) in the opposite direction. What I do know, however, is that I have had a terrific journey—still in full swing—since reporting to work at Chevron Oil Field Research Company on Monday, October 7, 1974. Looking Back My career has spanned three distinct experiences in the oil industry— international oil company (IOC), national oil company (NOC), and now entrepreneurship. In September 2007, I launched the third and present phase of my career as a founder of Quantum Reservoir Impact—a niche-technology, venture-capital startup. My career can be viewed as a grand mosaic with three complementary segments, each with its unique color and accent.

Quantum Nonequilibrium Steady States Induced by Repeated Interactions

We study the steady state of a finite XX chain coupled at its boundaries to quantum reservoirs made of free spins that interact one after the other with the chain. The two-point correlations are calculated exactly, and it is shown that the steady state is completely characterized by the magnetization profile and the associated current. Except at the boundary sites, the magnetization is given by the average of the reservoirs' magnetizations. The steady-state current, proportional to the difference in the reservoirs' magnetizations, shows a nonmonotonic behavior with respect to the system-reservoir coupling strength, with an optimal current state for a finite value of the coupling. Moreover, we show that the steady state can be described by a generalized Gibbs state.

Dissipation of classical energy in nonlinear quantum systems

We show using two simple nonlinear quantum systems that the infinite set of quantum dynamical variables, as introduced in quantized Hamilton dynamics [O. V. Prezhdo and Y. V. Pereverzev, J. Chem. Phys. 113, 6557 (2000)], behave as a thermostat with respect to the finite number of classical variables. The coherent classical component of the evolution decays by coupling to the chaotic quantum reservoir. The classical energy, understood as the part of system energy expressible through the average values of coordinates and momenta, is transferred to the quantum energy expressible through the higher moments of coordinates and momenta and other quantum variables. At long times, the classical variables reach equilibrium, and the classical energy fluctuates around the equilibrium value. These phenomena are illustrated with the exactly solvable Jaynes-Cummings model and a nonlinear oscillator.

Functional integral treatment of some quantum nondemolition systems

In the scheme of a quantum nondemolition (QND) measurement, an observable is measured without perturbing its evolution. In the context of studies of decoherence in quantum computing, we examine the ‘open’ quantum system of a two-level atom or, equivalently, a spin-1/2 system, in interaction with quantum reservoirs of either oscillators or spins, under the QND condition of the Hamiltonian of the system commuting with the system–reservoir interaction. For completeness, we also examine the well-known non-QND spin-Bose problem. For all these many-body systems, we use the methods of functional integration to work out the propagators. The propagators for the QND Hamiltonians are shown to be analogous to the squeezing and rotation operators, respectively, for the two kinds of baths considered. Squeezing and rotation being both phase-space area-preserving canonical transformations, this brings out an interesting connection between the energy-preserving QND Hamiltonians and the homogeneous linear canonical transformations.

Transition from phase slips to the Josephson effect in a superfluid 4He weak link

The rich dynamics of flow between two weakly coupled macroscopic quantum reservoirs has led to a range of important technologies. Practical development has so far been limited to superconducting systems, for which the basic building block is the so-called superconducting Josephson weak link. With the recent observation of quantum oscillations in superfluid 4He near 2K, we can now envision analogous practical superfluid helium devices. The characteristic function which determines the dynamics of such systems is the current-phase relation Is(phi), which gives the relationship between the superfluid current Is flowing through a weak link and the quantum phase difference phi across it. Here we report the measurement of the current-phase relation of a superfluid 4He weak link formed by an array of nano-apertures separating two reservoirs of superfluid 4He. As we vary the coupling strength between the two reservoirs, we observe a transition from a strongly coupled regime in which Is(phi) is linear and flow is limited by 2pi phase slips, to a weak coupling regime where Is(phi) becomes the sinusoidal signature of a Josephson weak link.

Unconditional preparation of entanglement between atoms in cascaded optical cavities.

We propose a scheme to unconditionally entangle the internal states of atoms trapped in separate high-finesse optical cavities. The scheme uses the technique of quantum reservoir engineering in a cascaded cavity-QED setting, and for ideal (lossless) coupling between the cavities generates an entangled pure state. Highly entangled states are also shown to be possible for realizable cavity-QED parameters and with nonideal coupling.

Dynamical description of quantum computing: Generic nonlocality of quantum noise

We develop a dynamical non-Markovian description of quantum computing in the weak-coupling limit, in the lowest-order approximation. We show that the long-range memory of the quantum reservoir (such as the ${1/t}^{4}$ one exhibited by electromagnetic vacuum) produces a strong interrelation between the structure of noise and the quantum algorithm, implying nonlocal attacks of noise. This shows that the implicit assumption of quantum error correction theory---independence of noise and self-dynamics---fails in long time regimes. We also use our approach to present pure decoherence and decoherence accompanied by dissipation in terms of the spectral density of the reservoir. The so-called dynamical decoupling method is discussed in this context. Finally, we propose a minimal decoherence model, in which the only source of decoherence is vacuum. We optimize the fidelity of quantum-information processing under the trade-off between the speed of the gate and the strength of decoherence.

Theory of pseudomodes in quantum optical processes

This paper deals with non-Markovian behaviour in atomic systems coupled to a structured reservoir of quantum EM field modes, with particular relevance to atoms interacting with the field in high Q cavities or photonic band gap materials. In cases such as the former, we show that the pseudo mode theory for single quantum reservoir excitations can be obtained by applying the Fano diagonalisation method to a system in which the atomic transitions are coupled to a discrete set of (cavity) quasimodes, which in turn are coupled to a continuum set of (external) quasimodes with slowly varying coupling constants and continuum mode density. Each pseudomode can be identified with a discrete quasimode, which gives structure to the actual reservoir of true modes via the expressions for the equivalent atom-true mode coupling constants. The quasimode theory enables cases of multiple excitation of the reservoir to now be treated via Markovian master equations for the atom-discrete quasimode system. Applications of the theory to one, two and many discrete quasimodes are made. For a simple photonic band gap model, where the reservoir structure is associated with the true mode density rather than the coupling constants, the single quantum excitation case appears to be equivalent to a case with two discrete quasimodes.

Non-Markovian Quantum Optical Processes and Pseudomodes

Non-Markovian behaviour in atomic systems coupled to a structured reservoir of quantum EM field modes, such as in high Q cavities, is treated using a quasimode description, and the pseudo mode theory for single quantum reservoir excitations is obtained via Fano diagonalisation. The atomic transitions are coupled to a discrete set of (cavity) quasimodes, which are also coupled to a continuum set of (external) quasimodes with slowly varying coupling constants. Each pseudomode corresponds to a cavity quasimode, and the original reservoir structure is obtained in expressions for the equivalent atom-true mode coupling constants. Cases of multiple excitation of the reservoir are now treatable via Markovian master equations for the atom-discrete quasimode system.

Nonlinear resonant tunneling in systems coupled to quantum reservoirs

An adiabatic approximation in terms of instantaneous resonances is developed to study the steady-state and time-dependent transport of interacting electrons in biased resonant tunneling heterostructures. The resulting model consists of quantum reservoirs coupled to regions where the system is described by nonlinear ordinary differential equations and has a general conceptual interest.

Quantum Reservoir Engineering with Laser Cooled Trapped Ions.

We show how to design different couplings between a single ion trapped in a harmonic potential and an environment. The coupling is due to the absorption of a laser photon and subsequent spontaneous emission. The variation of the laser frequencies and intensities allows one to ``engineer'' the coupling and select the master equation describing the motion of the ion.

The Dynamics of Classical Spins Interacting with Pump Field and Quantum Reservoir

A model of classical spins driven by an external alternating field and coupled to a quantum heat bath (a free Bose field) is investigated. An approach based on the Alexandrov method combined with the Zubarev formalism is applied. Evolution equations for the nonequilibrium mean values of three components of the density spin are derived in the limit of a weak coupling between spins and thermal reservoir. The difference between the model considered and its quantum counterpart is discussed.