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Klaus Mølmer

Publications and source records attributed to Klaus Mølmer.

At least 163 records · Page 9Linked to original sources
arXiv2014

How bosonic is a pair of fermions?

Composite particles made of two fermions can be treated as ideal elementary bosons as long as the constituent fermions are sufficiently entangled. In that case, the Pauli principle acting on the parts does not jeopardise the bosonic behaviour of the whole. An indicator for bosonic quality is the composite boson normalisation ratio $χ_{N+1}/χ_{N}$ of a state of $N$ composites. This quantity is prohibitively complicated to compute exactly for realistic two-fermion wavefunctions and large composite numbers $N$. Here, we provide an efficient characterisation in terms of the purity $P$ and the largest eigenvalue $λ_1$ of the reduced single-fermion state. We find the states that extremise $χ_N$ for given $P$ and $λ_1$, and we provide easily evaluable, saturable upper and lower bounds for the normalisation ratio. Our results strengthen the relationship between the bosonic quality of a composite particle and the entanglement of its constituents.

quant-ph↗
arXiv2013

Two-boson composites

Composite bosons made of two bosonic constituents exhibit deviations from ideal bosonic behavior due to their substructure. This deviation is reflected by the normalization ratio of the quantum state of N composites. We find a set of saturable, efficiently evaluable bounds for this indicator, which quantifies the bosonic behavior of composites via the entanglement of their constituents. We predict an abrupt transition between ordinary and exaggerated bosonic behavior in a condensate of two-boson composites.

quant-ph↗
arXiv2013

Fidelity of Fock-state-encoded qubits subjected to continuous variable Gaussian processes

When a harmonic oscillator is under the influence of a Gaussian process such as linear damping, parametric gain, and linear coupling to a thermal environment, its coherent states are transformed into states with Gaussian Wigner function. Qubit states can be encoded in the |0> and |1> Fock states of a quantum harmonic oscillator, and it is relevant to know the fidelity of the output qubit state after a Gaussian process on the oscillator. In this paper we present a general expression for the average qubit fidelity in terms of the first and second moments of the output from input coherent states subjected to Gaussian processes.

quant-ph↗
arXiv2013

Off-resonant transitions in the collective dynamics of multilevel atomic ensembles

We study the contributions of off-resonant transitions to the dynamics of a system of N multilevel atoms sharing one excitation and interacting with the quantized vector electromagnetic field. The Rotating Wave Approximation significantly simplifies the derivation of the equations of motion describing the collective atomic dynamics, but it leads to an incorrect expression for the dispersive part of the atom-atom interaction terms. For the case of two-level atoms and a scalar electromagnetic field, it turns out that the atom-atom interaction can be recovered correctly if integrals over the photon mode frequencies are extended to incorporate negative values. We explicitly derive the atom-atom interaction for multi-level atoms, coupled to the full vector electromagnetic field, and we recover also in this general case the validity of the results obtained by the extension to negative frequencies of the formulas derived with the Rotating Wave Approximation.

quant-ph↗
arXiv2013

Robust Rydberg interaction gates with adiabatic passage

We show that with adiabatic passage, one can reliably drive two-photon optical transitions between the ground states and interacting Rydberg states in a pair of atoms. For finite Rydberg interaction strengths a new adiabatic pathway towards the doubly Rydberg excited state is identified when a constant detuning is applied with respect to an intermediate optically excited level. The Rydberg interaction among the excited atoms provides a phase that may be used to implement quantum gate operations on atomic ground state qubits.

quant-ph↗
arXiv2013

Fundamental limitations in spin-ensemble quantum memories for cavity fields

Inhomogeneously broadened spin ensembles play an important role in present-day implementation of hybrid quantum processing architectures. When coupled to a resonator such an ensemble may serve as a multi-mode quantum memory for the resonator field, and by employing spin-refocusing techniques the quantum memory time can be extended to the coherence time of individual spins in the ensemble. In the present paper we investigate such a memory protocol capable of storing an unknown resonator-field state, and we examine separately the various constituents of the protocol: the storage and read-out part, the memory hold time with the spin ensemble and resonator field decoupled, and the parts employing spin refocusing techniques. Using both analytical and numerical methods we derive how the obtainable memory performance scales with various physical parameters.

quant-ph↗
arXiv2013

Process Characterisation with Monte-Carlo Wave-Functions

We present a numerically efficient method for the characterisation of a quantum process subject to dissipation and noise. The master equation evolution of a maximally entangled state of the quantum system and a non-evolving ancilla system is simulated by Monte-Carlo wave-functions. We show how each stochastic state vectors provides quantities that are readily combined into an average process χ-matrix. Our method significantly reduces the computational complexity in comparison with standard characterisation methods. It also readily provides an upper bound on the trace distance between the ideal and simulated process based on the evolution of only a single wave function of the entangled system.

quant-ph↗
arXiv2013

Dark Entangled Steady States of Interacting Rydberg Atoms

We propose a scheme for rapid generation of high fidelity steady state entanglement between a pair of atoms. A two-photon excitation process towards long-lived Rydberg states with finite pairwise interaction, a dark state interference effect in the individual atoms, and spontaneous emission from their short-lived excited states lead to rapid, dissipative formation of an entangled steady state. We show that for a wide range of physical parameters, this entangled state is formed on a time scale given by the strengths of coherent Raman and Rabi fields applied to the atoms, while it is only weakly dependent on the Rydberg interaction strength.

quant-ph↗
arXiv2013

Past quantum states

A density matrix ρ(t) yields probabilistic information about the outcome of measurements on a quantum system. We introduce here the past quantum state, which, at time T, accounts for the state of a quantum system at earlier times t < T. The past quantum state Ξ(t) is composed of two objects, ρ(t) and E(t), conditioned on the dynamics and the probing of the system until t and in the time interval [t, T], respectively. The past quantum state is characterized by its ability to make better predictions for the unknown outcome of projective and weak value measurements at t than the conventional quantum state at that time. On the one hand, our formalism shows how smoothing procedures for estimation of past classical signals by a quantum probe [M. Tsang, Phys. Rev. Lett. 102, 250403, (2009)] apply also to describe the past state of the quantum system itself. On the other hand, it generalizes theories of pre- and post-selected quantum states [Y. Aharonov and L. Vaidman, J. Phys. A: Math. Gen. 24, 2315 (1991)] to systems subject to any quantum measurement scenario, any coherent evolution, and any Markovian dissipation processes.

quant-ph↗
arXiv2013

Effective description of tunneling in a time-dependent potential with applications to voltage switching in Josephson junctions

We propose to use a time-dependent imaginary potential to describe quantum mechanical tunneling through time-varying potential barriers. We use Gamow solutions for stationary tunneling problems to justify our choice of potential, and we apply our method to describe tunneling of a mesoscopic quantum variable: the phase change across a Josephson junction. The Josephson junction phase variable behaves as the position coordinate of a particle moving in a tilted washboard potential, and our general solution to the motion in such a potential with a time-dependent tilt reproduces a number of features associated with voltage switching in Josephson junctions. Apart from applications as artificial atoms in quantum information studies, the Josephson junction may serve as an electric field sensitive detector, and our studies provide a detailed understanding of how the voltage switching dynamics couples to the electric field amplitude.

quant-ph↗
arXiv2013

Non-adiabatic many-atom quantum state control in few-well systems

We present a fast scheme for arbitrary unitary control of interacting bosonic atoms in a double-well. Assuming fixed inter-well tunnelling rate and intra-well interaction strength, we control the many-atom state by a discrete sequence of shifts of the single-well energies. For strong interactions, resonant tunnelling transitions implement beam-splitter U(2) rotations among atom number eigenstates, which can be combined and, thus, permit full controllability. By numerically optimizing such sequences of couplings at avoided level crossings (CALC), we extend the realm of full controllability to a wide range of realistic interaction parameters, while we remain in the simple control space. We demonstrate the efficiency and the high achievable fidelity of our proposal with non-adiabatic population transfer, N00N-state creation, a C-NOT gate, and a transistor-like, conditional evolution of several atoms.

quant-ph↗
arXiv2013

Quantum memory for microwave photons in an inhomogeneously broadened spin ensemble

We propose a multi-mode quantum memory protocol able to store the quantum state of the field in a microwave resonator into an ensemble of electronic spins. The stored information is protected against inhomogeneous broadening of the spin ensemble by spin-echo techniques resulting in memory times orders of magnitude longer than previously achieved. By calculating the evolution of the first and second moments of the spin-cavity system variables for realistic experimental parameters, we show that a memory based on NV center spins in diamond can store a qubit encoded on the |0> and |1> Fock states of the field with 80% fidelity.

quant-ph↗
arXiv2013

Dynamical effects of exchange symmetry breaking in mixtures of interacting bosons

In a double-well potential, a Bose-Einstein condensate exhibits Josephson oscillations or self-trapping, depending on its initial preparation and on the ratio of inter-particle interaction to inter-well tunneling. Here, we elucidate the role of the exchange symmetry for the dynamics with a mixture of two distinguishable species with identical physical properties, i.e. which are governed by an isospecific interaction and external potential. In the mean-field limit, the spatial population imbalance of the mixture can be described by the dynamics of a single species in an effective potential with modified properties or, equivalently, with an effective total particle number. The oscillation behavior can be tuned by populating the second species while maintaining the spatial population imbalance and all other parameters constant. In the corresponding many-body approach, the single-species description approximates the full counting statistics well also outside the realm of spin-coherent states. The method is extended to general Bose-Hubbard systems and to their classical mean-field limits, which suggests an effective single-species description of multicomponent Bose gases with weakly an-isospecific interactions.

cond-mat.quant-gas↗
arXiv2012

Bayesian parameter inference from continuously monitored quantum systems

We review the introduction of likelihood functions and Fisher information in classical estimation theory, and we show how they can be defined in a very similar manner within quantum measurement theory. We show that the stochastic master equations describing the dynamics of a quantum system subject to a definite set of measurements provides likelihood functions for unknown parameters in the system dynamics, and we show that the estimation error, given by the Fisher information, can be identified by stochastic master equation simulations. For large parameter spaces we describe and illustrate the efficient use of Markov Chain Monte Carlo sampling of the likelihood function.

quant-ph↗
arXiv2012

Impulsive Laser Induced Alignment of Molecules Dissolved in Helium Nanodroplets

We show that a 450 fs nonresonant, moderately intense, linearly polarized laser pulse can induce field-free molecular axis alignment of methyliodide molecules dissolved in a helium nanodroplet. Time-resolved measurements reveal rotational dynamics much slower than that of isolated molecules and, surprisingly, complete absence of the sharp transient alignment recurrences characteristic of gas phase molecules. Our results presage a range of new opportunities for exploring both molecular dynamics in a dissipative environment and the properties of He nanodroplets.

physics.chem-ph↗
arXiv2012

Collective interference of composite two-fermion bosons

The composite character of two-fermion bosons manifests itself in the interference of many composites as a deviation from the ideal bosonic behavior. A state of many composite bosons can be represented as a superposition of different numbers of perfect bosons and fermions, which allows us to provide the full Hong-Ou-Mandel-like counting statistics of interfering composites. Our theory quantitatively relates the deviation from the ideal bosonic interference pattern to the entanglement of the fermions within a single composite boson.

quant-ph↗
arXiv2012

Estimation of classical parameters via continuous probing of complementary quantum observables

We discuss how continuous probing of a quantum system allows estimation of unknown classical parameters embodied in the Hamiltonian of the system. We generalize the stochastic master equation associated with continuous observation processes to a Bayesian filter equation for the probability distribution of the desired parameters, and we illustrate its application by estimating the direction of a magnetic field. In our example, the field causes a ground state spin precession in a two-level atom which is detected by the polarization rotation of off-resonant optical probes, interacting with the atomic spin components.

quant-ph↗