Quantum Optical Systems Research Articles

Non-Markovian waiting-time distribution for quantum jumps in open systems

Simulation methods based on stochastic realizations of state vector evolutions are commonly used tools to solve open quantum system dynamics, both in the Markovian and non-Markovian regime. Here, we address the question of waiting time distribution (WTD) of quantum jumps for non-Markovian systems. We generalize Markovian quantum trajectory methods in the sense of deriving an exact analytical WTD for non-Markovian quantum dynamics and show explicitly how to construct this distribution for certain commonly used quantum optical systems.

Capacities of linear quantum optical systems

A wide variety of communication channels employ the quantized electromagnetic field to convey information. Their communication capacity crucially depends on losses associated to spatial characteristics of the channel such as diffraction and antenna design. Here we focus on the communication via a finite pupil, showing that diffraction is formally described as a memory channel. By exploiting this equivalence we then compute the communication capacity of an optical refocusing system, modeled as a converging lens. Even though loss of information originates from the finite pupil of the lens, we show that the presence of the refocusing system can substantially enhance the communication capacity. We mainly concentrate on communication of classical information, the extension to quantum information being straightforward.

Master Equations for Correlated Quantum Channels

We derive the general form of a master equation describing the reduced time evolution of a sequence of subsystems "propagating" in an environment which can be described as a sequence of subenvironments. The interaction between subsystems and subenvironments is described in terms of a collision model, with the irreversible dynamics of the subenvironments between collisions explicitly taken into account. In the weak coupling regime, we show that the collisional model produces a correlated Markovian evolution for the joint density matrix of the multipartite system. The associated Lindblad superoperator contains pairwise terms describing cross correlation between the different subsystems. Such a model can describe a broad range of physical situations, ranging from quantum channels with memory to photon propagation in concatenated quantum optical systems.

Thermodynamics of Information Processing in Small Systems*)

We review a general theory of thermodynamics of information processing. The background of this topic is the recently-developed nonequilibrium statistical mechanics and quantum (and classical) information theory. These theories are closely related to the modern technologies to manipulate and observe small systems; for example, macromolecules and colloidal particles in the classical regime, and quantum-optical systems and quantum dots in the quantum regime. First, we review a generalization of the second law of thermodynamics to the situations in which small thermodynamic systems are subject to quantum feedback control. The generalized second law is expressed in terms of an inequality that includes the term of information obtained by the measurement, as well as the thermodynamic quantities such as the free energy. This inequality leads to the fundamental upper bound of the work that can be extracted by a “Maxwell's demon”, which can be regarded as a feedback controller with a memory that stores measurement outcomes. Second, we review generalizations of the second law of thermodynamics to the measurement and information erasure processes of the memory of the demon that is a quantum system. The generalized second laws consist of inequalities that identify the lower bounds of the energy costs that are needed for the measurement and the information erasure. The inequality for the erasure leads to the celebrated Landauer's principle for a special case. Moreover, these inequalities enable us to reconcile Maxwell's demon with the second law of thermodynamics. In these inequalities, thermodynamic quantities and information contents are treated on an equal footing. In fact, the inequalities are model-independent, so that they can be applied to a broad class of information processing. Therefore, these inequalities can be called the second law of “information thermodynamics”.

Active control of electromagnetically induced transparency analogue in terahertz metamaterials

Recently reported metamaterial analogues of electromagnetically induced transparency enable a unique route to endow classical optical structures with aspects of quantum optical systems. This method opens up many fascinating prospects on novel optical components, such as slow light units, highly sensitive sensors and nonlinear devices. In particular, optical control of electromagnetically induced transparency in metamaterials promises essential application opportunities in optical networks and terahertz communications. Here we present active optical control of metamaterial-induced transparency through active tuning of the dark mode. By integrating photoconductive silicon into the metamaterial unit cell, a giant switching of the transparency window occurs under excitation of ultrafast optical pulses, allowing for an optically tunable group delay of the terahertz light. This work opens up the possibility for designing novel chip-scale ultrafast devices that would find utility in optical buffering and terahertz active filtering.

Coherent Feedback Control of Linear Quantum Optical Systems via Squeezing and Phase Shift

The purpose of this paper is to present a theoretic and numerical study of utiliz- ing squeezing and phase shift in coherent feedback control of linear quantum optical systems. A quadrature representation with built-in phase shifters is proposed for such systems. Fundamen- tal structural characterizations of linear quantum optical systems are derived in terms of the new quadrature representation. These results reveal considerable insights into the issue of the physical realizability of such quantum systems. The problem of coherent quantum linear quadratic Gaussian (LQG) feedback control studied in H. I. Nurdin, M. R. James, and I. R. Petersen, Automatica, IFAC, 45 (2009), pp. 1837-1846; G. Zhang and M. R. James, IEEE Trans. Automat. Control, 56 (2011), pp. 1535-1550 is reinvestigated in depth. First, the optimization methods in these papers are extended to a multistep optimization algorithm which utilizes ideal squeezers. Second, a two-stage optimization approach is proposed on the basis of controller parametrization. Numerical studies show that closed-loop systems designed via the second approach may offer LQG control performance even better than that when the closed-loop systems are in the vacuum state. When ideal squeezers in a closed-loop system are replaced by (more realistic) degenerate parametric amplifiers, a sufficient condition is derived for the asymptotic stability of the resultant new closed-loop system; the issue of performance convergence is also discussed in the LQG control setting.

Quantum encoding based on optical phase states and mutually unbiased bases in the presence of several eavesdroppers

We investigate quantum key distribution where information is carried by a d-level optical quantum system. The sender uses the mutually unbiased bases generated from the phase states of the quantum system. We consider the effects of several intercept and resend attacks. We derive explicitly the mutual information between the legitimate parties as well as the mutual information between the sender and the different eavesdroppers in the communication channel. We discuss the security of the cryptographic scheme and present some numerical analysis.

Prospects of quantum information processing with atoms

Quantum information, and particular questions of implementing quantum information processing, is now almost two decades old, and has developed into a mature field of physics. In the first decade many of the conceptual foundations of the field of quantum information were laid down, many of the basic theoretical proposals for implementing quantum computing and quantum communications with various physical systems were formulated, and a first generation of experimental demonstrations of some of the basic building blocks and protocols of QIPC were shown in the lab. Today we are in a phase where the experimental challenge is not only to achieve high fidelity in operations, but to scale up systems both in the number of qubits and in the complexity of the quantum operations towards fault tolerant quantum computing. Progress during the last few years has been remarkable, and exceeded our early dreams, although on the scale of futuristic goals and hopes of QIPC this remains a first step. The requirements of implementing QIPC include the manipulation of many particle quantum systems on the level of single quanta, the ability to prepare and read out quantum states with high fidelity, while achieving complete isolation from the environment. Quantum optical systems of trapped ions, atoms, molecules and photons, as in CQED, have always had a leading role in achieving these goals. The rapid progress in achieving quantum control in many particle physics happens, of course, in a much broader context, and solid state systems such as superconducting qubits, quantum dots and NV centers, as well as circuit QED and nanomechanics are becoming serious contenders for atomic systems. The present issue focuses on quantum information processing with neutral atoms and molecules. What do we see as interesting future directions and possibilities?

Connecting two jumplike unravelings for non-Markovian open quantum systems

The development and use of Monte Carlo algorithms plays a visible role in the study of non-Markovian quantum dynamics due to the provided insight and powerful numerical methods for solving the system dynamics. In the Markovian case, the connections between the various types of methods are fairly well understood while, for the non-Markovian case, there has so far been only a few studies. We focus here on two jumplike unravelings of non-Markovian dynamics: the non-Markovian quantum jump (NMQJ) method and the property state method by Gambetta, Askerud, and Wiseman (GAW). The results for simple quantum optical systems illustrate the connections between the realizations of the two methods and also highlight how the probability currents between the system and environment, or between the property states of the total system, are associated with the decay rates of time-local master equations and, consequently, with the jump rates of the NMQJ method.

Quantum Fluctuations of Low Dimensional Bose-Einstein Condensates in Optical Systems

A system of low dimensional condensed ultracold atomic gases inside a field of a laser-driven optical cavity exhibits dispersive optical bistability. During such a process the system also shows quantum fluctuations. Condensate fluctuations are highly manifested particularly in low dimensional systems. In this paper we have investigated the theory and manifestation of fluctuations in quantum optical systems in low dimensional Bose-Einstein condensates. We have described the system using the mean-field approximation. In this study we have verified that low dimensional quantum gases exhibit not only highly fascinating properties but also we have indicated that the use of mean field theory to describe quantum gases in low dimensions is highly restricted since the possibility of generating low dimensional bosonic condensates is dominated by the existence of highly sensitive and intrinsic quantum fluctuations.

Few-photon transport in low-dimensional systems

We analyze the role of quantum interference effects induced by an embedded two-level system on the photon transport properties in waveguiding structures that exhibit cutoffs (band edges) in their dispersion relation. In particular, we demonstrate that these systems invariably exhibit single-particle photon-atom bound states and strong effective nonlinear responses on the few-photon level. Based on this, we find that the properties of these photon-atom bound states may be tuned via the underlying dispersion relation and that their occupation can be controlled via multiparticle scattering processes. This opens an interesting route for controlling photon transport properties in a number of solid-state-based quantum optical systems and the realization of corresponding functional elements and devices.

Coherence properties of a single dipole emitter in diamond

On-demand, high repetition rate sources of indistinguishable, polarized single photons are the key component for future photonic quantum technologies (O'Brien et al 2009 Nat. Photonics3 687–95). Colour centres in diamond offer a promising solution, and the narrow linewidth of the recently identified nickel-based NE8 centre makes it particularly appealing for realizing the transform-limited sources necessary for quantum interference. Here, we report the characterization of dipole orientation and coherence properties of a single NE8 colour centre in a diamond nanocrystal at room temperature. We observe a single-photon coherence time of 0.21 ps and an emission lifetime of 1.5 ns. Combined with an emission wavelength that is ideally suited for applications in existing quantum optical systems, these results show that NE8 is a far more promising source than the more commonly studied nitrogen-vacancy centre and point the way to the realization of a practical diamond colour centre-based single-photon source.

Quantum stochastic differential equations and continuous measurements: unbounded coefficients

A natural formulation of the theory of quantum measurements in continuous time is based on quantum stochastic differential equations (Hudson-Parthasarathy equations). However, such a theory was developed only in the case of Hudson-Parthasarathy equations with bounded coefficients. By using some results on Hudson-Parthasarathy equations with unbounded coefficients, we are able to extend the theory of quantum continuous measurements to cases in which unbounded operators on the system space are involved. A significant example of a quantum optical system (the degenerate parametric oscillator) is shown to fulfill the hypotheses introduced in the general theory.

Non-Markovian dynamics of a nanomechanical resonator measured by a quantum point contact

We study the dynamics of a nanomechanical resonator (NMR) subject to a measurement by a low-transparency quantum point contact (QPC) or tunnel junction in the non-Markovian domain. We derive the non-Markovian number-resolved (conditional) and unconditional master equations valid to second order in the tunneling Hamiltonian without making the rotating-wave approximation and the Markovian approximation, generally made for systems in quantum optics. Our non-Markovian master equation reduces, in appropriate limits, to various Markovian versions of master equations in the literature. We find considerable difference in dynamics between the non-Markovian case and its Markovian counterparts. We also calculate the time-dependent transport current through the QPC, which contains information about the measured NMR system. We find an extra transient current term proportional to the expectation value of the symmetrized product of the position and momentum operators of the NMR. This extra current term, with a coefficient coming from the combination of the imaginary parts of the QPC reservoir correlation functions, has a substantial contribution to the total transient current in the non-Markovian case, but was generally ignored in the studies of the same problem in the literature. Considering the contribution of this extra term, we show that a significant qualitative and quantitative difference in the total transient current between the non-Markovian and the Markovian wideband-limit cases can be observed. Thus, it may serve as a witness or signature of the non-Markovian features in the coupled NMR-QPC system.

Simulating quantum-optical phenomena with cold atoms in optical lattices

We propose a scheme involving cold atoms trapped in optical lattices to observe different phenomena traditionally linked to quantum-optical systems. The basic idea consists of connecting the trapped atomic state to a non-trapped state through a Raman scheme. The coupling between these two types of atoms (trapped and free) turns out to be similar to that describing light–matter interaction within the rotating-wave approximation, the role of matter and photons being played by the trapped and free atoms, respectively. We explain in particular how to observe phenomena arising from the collective spontaneous emission of atomic and harmonic oscillator samples, such as superradiance and directional emission. We also show how the same setup can simulate Bose–Hubbard Hamiltonians with extended hopping as well as Ising models with long-range interactions. We believe that this system can be realized with state of the art technology.

Rare-earth-doped materials for applications in quantum information storage and signal processing

Realization of practical quantum memory and optical signal processing systems critically depends on suitable materials that offer specific combinations of properties. Solid-state materials such as rare-earth ions doped into dielectric crystals are one of the most promising candidates for several quantum information storage protocols, including quantum storage of single photons. This article provides an overview of rare-earth-doped material properties and summarizes some of the most promising materials studied in our laboratory and by other groups for applications in quantum information storage and for ultra-wide bandwidth signal processing. Understanding and controlling spectral diffusion in these materials, which ultimately limits the achievable performance of any quantum memory system, is also briefly reviewed. Applications in quantum information impose stringent requirements on laser phase and frequency stability, and employing a narrow spectral hole in the inhomogeneous absorption profile in these materials as a frequency reference can dramatically improve laser stability. We review our work on laser frequency and phase stabilization and report our recent results on using a narrow spectral hole as a passive dynamic spectral filter for laser phase noise suppression, which can dramatically narrow the laser linewidth with or without the requirement of active feedback.

Hamiltonian Control of Quantum Dynamical Semigroups: Stabilization and Convergence Speed

We consider finite-dimensional Markovian open quantum systems, and characterize the extent to which time-independent Hamiltonian control may allow to stabilize a target quantum state or subspace and optimize the resulting convergence speed. For a generic Lindblad master equation, we introduce a dissipation-induced decomposition of the associated Hilbert space, and show how it serves both as a tool to analyze global stability properties for given control resources and as the starting point to synthesize controls that ensure rapid convergence. The resulting design principles are illustrated in realistic Markovian control settings motivated by quantum information processing, including quantum-optical systems and nitrogen-vacancy centers in diamond.

A Maxwell–Schrödinger solver for quantum optical few-level systems

The msprop program presented in this work is capable of solving the Maxwell–Schrödinger equations for one or several laser fields propagating through a medium of quantum optical few-level systems in one spatial dimension and in time. In particular, it allows to numerically treat systems in which a laser field interacts with the medium with both its electric and magnetic component at the same time. The internal dynamics of the few-level system is modeled by a quantum optical master equation which includes coherent processes due to optical transitions driven by the laser fields as well as incoherent processes due to decay and dephasing. The propagation dynamics of the laser fields is treated in slowly varying envelope approximation resulting in a first order wave equation for each laser field envelope function. The program employs an Adams predictor formula second order in time to integrate the quantum optical master equation and a Lax–Wendroff scheme second order in space and time to evolve the wave equations for the fields. The source function in the Lax–Wendroff scheme is specifically adapted to allow taking into account the simultaneous coupling of a laser field to the polarization and the magnetization of the medium. To reduce execution time, a customized data structure is implemented and explained. In three examples the features of the program are demonstrated and the treatment of a system with a phase-dependent cross coupling of the electric and magnetic field component of a laser field is shown. Program summary Program title: msprop Catalogue identifier: AEHR_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEHR_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 507 625 No. of bytes in distributed program, including test data, etc.: 10 698 552 Distribution format: tar.gz Programming language: C (C99 standard), Mathematica, bash script, gnuplot script Computer: Tested on x86 architecture Operating system: Unix/Linux environment RAM: Less than 30 MB Classification: 2.5 External routines: Standard C math library, accompanying bash script uses gnuplot, bc (basic calculator), and convert (ImageMagick) Nature of problem: We consider a system of quantum optical few-level atoms exposed to several near-resonant continuous-wave or pulsed laser fields. The complexity of the problem arises from the combination of the coherent and incoherent time evolution of the atoms and its dependence on the spatially varying fields. In systems with a coupling to the electric and magnetic field component the simultaneous treatment of both field components poses an additional challenge. Studying the system dynamics requires solving the quantum optical master equation coupled to the wave equations governing the spatio-temporal dynamics of the fields [1,2]. Solution method: We numerically integrate the equations of motion using a second order Adams predictor method for the time evolution of the atomic density matrix and a second order Lax–Wendroff scheme for iterating the fields in space [3]. For the Lax–Wendroff scheme, the source function is adapted such that a simultaneous coupling to the polarization and the magnetization of the medium can be taken into account. Restrictions: The evolution of the fields is treated in slowly varying envelope approximation [2] such that variations of the fields in space and time must be on a scale larger than the wavelength and the optical cycle. Propagation is restricted to the forward direction and to one dimension. Concerning the description of the atomic system, only a finite number of basis states can be treated and the laser-driven transitions have to be near-resonant such that the rotating-wave approximation can be applied [2]. Unusual features: The program allows the dipole interaction of both the electric and the magnetic component of a laser field to be taken into account at the same time. Thus, a system with a phase-dependent cross coupling of electric and magnetic field component can be treated (see Section 4.2 and [4]). Concerning the implementation of the data structure, it has been optimized for faster memory access. Compared to using standard memory allocation methods, shorter run times are achieved (see Section 3.2). Additional comments: Three examples are given. They each include a readme file, a Mathematica notebook to generate the C-code form of the quantum optical master equation, a parameter file, a bash script which runs the program and converts the numerical data into a movie, two gnuplot scripts, and all files that are produced by running the bash script. Running time: For the first two examples the running time is less than a minute, the third example takes about 12 minutes. On a Pentium 4 (3 GHz) system, a rough estimate can be made with a value of 1 second per million grid points and per field variable.

Quantum phase transition and excitations of the Tavis-Cummings lattice model

The enormous progress in controlling quantum optical and atomic systems has prompted ideas for new experimental realizations of strongly correlated many-body systems operating with light. These systems consist of photons confined in optical cavities, which interact strongly with atoms or atomiclike structures. Due to the interaction between the two particle species optical nonlinearities appear, leading to a quantum phase transition from Mott to superfluid phase. Here, we address the Tavis-Cummings lattice model, which describes light-matter systems containing multiple atomiclike structures in each cavity. In particular, we investigate the phase boundary delimiting Mott from superfluid phase and the elementary excitations of the two-dimensional Tavis-Cummings lattice model in dependence of the number of atomiclike structures per cavity. In order to obtain the results we employ the variational cluster approach. We evaluate spectral functions and densities of states of both particle species, which allows us to characterize the fundamental excitations of light-matter systems. These excitations are termed polaritons and are superpositions of photons and atomic excitations. We introduce polariton quasiparticles as appropriate linear combinations of both particle species and analyze the weights of their constituents. Our results demonstrate the dependence of the quantum phase transition and the elementary excitations on the number of atomiclike structures per cavity and provide thus valuable insight into the physics of light-matter systems.

Excitations of Strongly Correlated Lattice Polaritons

We present an analytic slave-boson approach to calculate the elementary excitations of the Jaynes-Cummings-Hubbard model (JCHM) describing strongly correlated polaritons on a lattice in various quantum optical systems. In the superfluid phase near the Mott transition we find a gapless, linear Goldstone mode and a gapped amplitude mode corresponding to phase and density fluctuations, respectively. The sound velocity of the Goldstone mode develops a peculiar anomaly as a function of detuning at low densities, which persists into the weakly interacting regime of a polariton BEC.