arXiv subjects

Klaus Mølmer

Publications and source records attributed to Klaus Mølmer.

At least 109 records · Page 6Linked to original sources

arXiv2018

Entangled Quantum Dynamics of Many-Body Systems using Bohmian Trajectories

Bohmian mechanics is an interpretation of quantum mechanics that describes the motion of quantum particles with an ensemble of deterministic trajectories. Several attempts have been made to utilize Bohmian trajectories as a computational tool to simulate quantum systems consisting of many particles, a very demanding computational task. In this paper, we present a novel ab-initio approach to solve the many-body problem for bosonic systems by evolving a system of one-particle wavefunctions representing pilot waves that guide the Bohmian trajectories of the quantum particles. In this approach, quantum entanglement effects arise due to the interactions between different configurations of Bohmian particles evolving simultaneously. The method is used to study the breathing dynamics and ground state properties in a system of interacting bosons.

quant-ph↗

arXiv2018

Critical slowing down of multi-atom entanglement by Rydberg blockade

Laser excitation pulses that lead to perfect adiabatic state transfer in an ensemble of three-level ladder atoms lead to highly entangled states of many atoms if their highest excited state is subject to Rydberg blockade. Solution of the Schrödinger equation shows that it is increasingly difficult to ensure the adiabatic evolution as the number of atoms increases. A diminishing energy gap, significant variations in collective observables, and increased work fluctuations link the critical slowing down of the adiabatic evolution with a quantum phase transition-like behavior of the system.

quant-ph↗

arXiv2018

Monte-Carlo Simulations of Superradiant Lasing

We present simulations of the superradiant dynamics of ensembles of atoms in the presence of collective and individual atomic decay processes. We unravel the density matrix with Monte-Carlo wave-functions and identify the quantum jumps in a reduced Dicke state basis, which reflects the permutation symmetry of the identical atoms. While the number of density matrix elements in the Dicke representation increases polynomially with atom number, the quantum jump dynamics populates only a single Dicke state at the time and thus efficient simulations can be carried out for tens of thousands of atoms. The calculated superradiance pulses from initially excited atoms agree quantitatively with recent experimental results with strontium atoms but rapid atom loss in these experiments does not permit steady-state superradiance. By introducing an incident flux of new atoms, the system can maintain a large average atom number, and our theoretical calculations predict lasing with millihertz linewidth despite rapid atom number fluctuations.

physics.optics↗

arXiv2018

Hypothesis testing with a continuously monitored quantum system

In a Bayesian analysis, the likelihood that specific candidate parameters govern the evolution of a quantum system are conditioned on the outcome of measurements which, in turn, cause measurement backaction on the state of the system [M. Tsang, Phys. Rev. Lett. 108, 170502 (2012)]. Specializing to the distinction of two candidate hypotheses, we study the achievements of continuous monitoring of the radiation emitted by a quantum system followed by an optimal projective measurement on its conditioned final state. Our study of the radiative decay of a driven two-level system shows an intricate interplay between the maximum information available from photon counting and homodyne detection and the final projective measurement on the emitter. We compare the results with theory predicting a lower bound for the probability to assign a wrong hypothesis by any combined measurement on the system and its radiative environment.

quant-ph↗

arXiv2018

Dicke Phase Transition in a Disordered Emitter-Graphene Plasmon System

We study the Dicke phase transition in a disordered system of emitters coupled to the plasmonic modes of a graphene monolayer. This system has unique properties associated with the tunable, dissipative and broadband characters of the graphene surface plasmons, as well as the disorder due to the random spatial distribution and the inhomogeneous line-width broadening of the emitters. We apply the Keldysh functional-integral approach, and identify a normal phase, a superradiant phase and a spin-glass phase of the system. The conditions for these phases and their experimental signatures are discussed.

quant-ph↗

arXiv2018

Multi-state and multi-hypothesis discrimination with open quantum systems

We show how an upper bound for the ability to discriminate any number N of candidates for the Hamiltonian governing the evolution of an open quantum system may be calculated by numerically efficient means. Our method applies an effective master equation analysis to evaluate the pairwise overlaps between candidate full states of the system and its environment pertaining to the Hamiltonians. These overlaps are then used to construct an N -dimensional representation of the states. The optimal positive-operator valued measure (POVM) and the corresponding probability of assigning a false hypothesis may subsequently be evaluated by phrasing optimal discrimination of multiple non-orthogonal quantum states as a semi-definite programming problem. We investigate the structure of the optimal POVM and we provide three realistic examples of hypothesis testing with open quantum systems.

quant-ph↗

arXiv2018

Precisely controlling the reflection phase of a photon via a strongly-coupled ancilla dressed qubit

We propose that Rydberg dressing of a single qubit atom can be used to control a surrounding ensemble of three-level atoms and hereby the phase of light reflected by an optical cavity. Our scheme employs an ensemble dark resonance that is perturbed by the qubit state of a single atom to yield a single-atom single-photon gate. We show here that off-resonant Rydberg dressing of the qubit offers experimentally-viable regimes of operation that drastically reduce error compared to schemes using shelved Rydberg population. Such low errors (in the $10^{-3}$ range) are a necessary condition for fault-tolerant optical-photon, gate-based quantum computation. We also demonstrate the technique for microwave circuit-QED, where a strongly-coupled ancilla superconducting qubit can be used in the place of the atomic ensemble to provide high-fidelity coupling to microwave photons.

quant-ph↗

arXiv2017

Fast state transfer in a Λ-system: a shortcut-to-adiabaticity approach to robust and resource optimized control

We propose an efficient strategy to find optimal control functions for state-to-state quantum control problems. Our procedure first chooses an input state trajectory, that can realize the desired transformation by adiabatic variation of the system Hamiltonian. The shortcut-to-adiabaticity (STA) formalism then provides a control Hamiltonian that realizes the reference trajectory exactly but on a finite time scale. As the final state is achieved with certainty, we define a cost functional that incorporates the resource requirements and a perturbative expression for robustness. We optimize this functional by systematically varying the reference trajectory. We demonstrate the method by application to population transfer in a laser driven three-level Λ-system, where we find solutions that are fast and robust against perturbations while maintaining a low peak laser power.

quant-ph↗

arXiv2017

Amplified emission and lasing in a plasmonic nano-laser with many three-level molecules

Steady-state plasmonic lasing is studied theoretically for a system consisting of many dye molecules arranged regularly around a gold nano-sphere. A three-level model with realistic molecular dissipation is employed to analyze the performance as function of the pump field amplitude and number of molecules. Few molecules and moderate pumping produce a single narrow emission peak because the excited molecules transfer energy to a single dipole plasmon mode by amplified spontaneous emission. Under strong pumping, the single peak splits into broader and weaker emission peaks because two molecular excited levels interfere with each other through coherent coupling with the pump field and with the dipole plasmon field. A large number of molecules gives rise to a Poisson-like distribution of plasmon number states with a large mean number characteristic of lasing action. These characteristics of lasing, however, deteriorate under strong pumping because of the molecular interference effect.

physics.optics↗

arXiv2017

Quantum parameter estimation with a neural network

We propose to use neural networks to estimate the rates of coherent and incoherent processes in quantum systems from continuous measurement records. In particular, we adapt an image recognition algorithm to recognize the patterns in experimental signals and link them to physical quantities. We demonstrate that the parameter estimation works unabatedly in the presence of detector imperfections which complicate or rule out Bayesian filter analyses.

quant-ph↗

arXiv2017

Relaxation of an ensemble of two-level emitters in a squeezed bath

We derive and evaluate equations of motion for the mean values and variances of the components of spins collectively coupled to a broadband squeezed radiation reservoir. Our formalism bridges between a single two-level emitter, represented by spin components that relax at different rates, depending on the degree of squeezing, to an ensemble of emitters represented by a large collective spin, whose components relax independently of the squeezing. For a single spin, the steady state fluctuations in the transverse components are independent of the squeezing, while the steady state of a large spin ensemble reflects the statistics of the squeezed reservoir. This follows from an analysis of the Langevin noise contributions to the equations of motion and their consequences for the first and second moments of the spin operators. We argue that the difference between a single and many spins is related to whether vacuum fluctuations or radiation reaction dominate the coupling of the spin system to the radiation environment.

quant-ph↗

arXiv2017

Prediction and retrodiction with continuously monitored Gaussian states

Gaussian states of quantum oscillators are fully characterized by the mean values and the covariance matrix of their quadrature observables. We consider the dynamics of a system of oscillators subject to interactions, damping, and continuous probing which maintain their Gaussian state property. Such dynamics is found in many physical systems that can therefore be efficiently described by the ensuing effective representation of the density matrix $ρ(t)$. Our probabilistic knowledge about the outcome of measurements on a quantum system at time $t$ is not only governed by $ρ(t)$ conditioned on the evolution and measurement outcomes obtained until time $t$, but is also modified by any information acquired after $t$. It was shown in [Phys. Rev. Lett. 111, 160401 (2013)] that this information is represented by a supplementary matrix, $E(t)$. We show here that the restriction of the dynamics of $ρ(t)$ to Gaussian states implies that the matrix $E(t)$ is also fully characterized by a vector of mean values and a covariance matrix. We derive the dynamical equations for these quantities and we illustrate their use in the retrodiction of measurements on Gaussian systems.

quant-ph↗

arXiv2017

Sequentially generated entanglement, macroscopicity and squeezing in a spin chain

We study quantum states generated by a sequence of nearest neighbor bipartite entangling operations along a one-dimensional chain of spin qubits. After a single sweep of such a set of operations, the system is effectively described by a matrix product state (MPS) with the same virtual dimension as the spin qubits. We employ the explicit form of the MPS to calculate expectation values and two-site correlation functions of local observables, and we use the results to study fluctuations of collective observables. Through the so-called macroscopicity and the squeezing properties of the collective spin variables they witness the quantum correlations and multi-particle entanglement within the chain. Macroscopicity only occurs over the entire chain if the nearest neighbor interaction is maximally entangling, while a finite, sequential interaction between nearest neighbor particles leads to squeezing of the collective spin.

quant-ph↗

arXiv2017

High-fidelity Rydberg quantum gate via a two-atom dark state

We propose a two-qubit gate for neutral atoms in which one of the logical state components adiabatically follows a two-atom dark state formed by the laser coupling to a Rydberg state and a strong, resonant dipole-dipole exchange interaction between two Rydberg excited atoms. Our gate exhibits optimal scaling of the intrinsic error probability $E \propto (Bτ)^{-1}$ with the interatomic interaction strength $B$ and the Rydberg state lifetime $τ$. Moreover, the gate is resilient to variations in the interaction strength, and even for finite probability of double Rydberg excitation, the gate does not excite atomic motion and experiences no decoherence due to internal-translational entanglement.

quant-ph↗

arXiv2017

Conditioned spin and charge dynamics of a single electron quantum dot

In this article we describe the incoherent and coherent spin and charge dynamics of a single electron quantum dot. We use a stochastic master equation to model the state of the system, as inferred by an observer with access to only the measurement signal. Measurements obtained during an interval of time contribute, by a past quantum state analysis, to our knowledge about the system at any time $t$ within that interval. Such analysis permits precise estimation of physical parameters, and we propose and test a modification of the classical Baum-Welch parameter re-estimation method to systems driven by both coherent and incoherent processes.

quant-ph↗

arXiv2017

Measurement of the topological Chern number by continuous probing of a qubit subject to a slowly varying Hamiltonian

We analyze a measurement scheme that allows determination of the Berry curvature and the topological Chern number of a Hamiltonian with parameters exploring a two-dimensional closed manifold. Our method uses continuous monitoring of the gradient of the Hamiltonian with respect to one parameter during a quasi-adiabatic quench of the other. Measurement back-action leads to disturbance of the system dynamics, but we show that this can be compensated by a feedback Hamiltonian. As an example, we analyze the implementation with a superconducting qubit subject to time varying, near resonant microwave fields; equivalent to a spin 1/2 particle in a magnetic field.

quant-ph↗

arXiv2017

Analysis of a multi-mode plasmonic nano-laser with an inhomogeneous distribution of molecular emitters

We extend Lamb's reduced density matrix laser theory to analyze the inhomogeneous molecular couplings and the mode-correlation in a plasmonic nano-laser consisting of a gold sphere and many dye molecules interacting with a driving optical field and with the quantized plasmon modes. The molecular inhomogeneity is accounted for by simulating their random distribution around the sphere. Our analysis shows that in order to obtain lasing we must employ a large number of strongly driven molecules to compensate strong damping of the plasmon modes. The compact molecular arrangement, however, can lead to molecular energy-shifts and thus reduce the excitation of the plasmon modes and ultimately suggests a maximum limit for the plasmon excitation for any specific system.

physics.optics↗

arXiv2017

Macroscopic realism of quantum work fluctuations

We study the fluctuations of the work performed on a driven quantum system, defined as the difference between subsequent measurements of energy eigenvalues. These work fluctuations are governed by statistical theorems with similar expressions in classical and quantum physics. In this article we show that we can distinguish quantum and classical work fluctuations, as the latter can be described by a macrorealistic theory and hence obey Leggett-Garg inequalities. We show that these inequalities are violated by quantum processes in a driven two-level system and in a harmonic oscillator subject to a squeezing transformation.

quant-ph↗