arXiv subjects

Klaus Mølmer

Publications and source records attributed to Klaus Mølmer.

At least 181 records · Page 10Linked to original sources

arXiv2012

Scattering of matter wave solitons on localized potentials

We present numerical and analytical results for the reflection and transmission properties of matter wave solitons impinging on localized scattering potentials in one spatial dimension. Our mean field analysis identifies regimes where the solitons behave more like waves or more like particles as a result of the interplay between the dispersive wave propagation and the attractive interactions between the atoms. For a bright soliton propagating together with a dark soliton void in a two-species Bose-Einstein condensate of atoms with repulsive interactions, we find different reflection and transmission properties of the dark and the bright components.

cond-mat.quant-gas↗

arXiv2012

Bosonic behavior of entangled fermions

Two bound, entangled fermions form a composite boson, which can be treated as an elementary boson as long as the Pauli principle does not affect the behavior of many such composite bosons. The departure of ideal bosonic behavior is quantified by the normalization ratio of multi-composite-boson states. We derive the two-fermion-states that extremize the normalization ratio for a fixed single-fermion purity P, and establish general tight bounds for this indicator. For very small purities, P<1/N^2, the upper and lower bounds converge, which allows to quantify accurately the departure from perfectly bosonic behavior, for any state of many composite bosons.

quant-ph↗

arXiv2012

Qudit Quantum Computation in the Jaynes-Cummings Model

We have developed methods for performing qudit quantum computation in the Jaynes-Cummings model with the qudits residing in a finite subspace of individual harmonic oscillator modes, resonantly coupled to a spin-1/2 system. The first method determines analytical control sequences for the one- and two-qudit gates necessary for universal quantum computation by breaking down the desired unitary transformations into a series of state preparations implemented with the Law-Eberly scheme. The second method replaces some of the analytical pulse sequences with more rapid numerically optimized sequences. In our third approach, we directly optimize the evolution of the system, without making use of any analytic techniques. While limited to smaller dimensional qudits, the third approach finds pulse sequences which carry out the desired gates in a time which is much shorter than either of the other two approaches.

quant-ph↗

arXiv2012

Shaking the entropy out of a lattice: atomic filtering by vibrational excitations

We present a simple and efficient scheme to reduce atom-number fluctuations in optical lattices. The interaction-energy difference for atoms in different vibrational states is used to remove excess atomic occupation. The remaining vacant sites are then filled with atoms by merging adjacent wells, for which we implement a protocol that circumvents the constraints of unitarity. The preparation of large regions with precisely one atom per lattice site is discussed for both bosons and fermions. The resulting low-entropy Mott-insulating states may serve as high-fidelity register states for quantum computing and as a starting point for investigations of many-body physics.

quant-ph↗

arXiv2012

Dynamical evolution of an inverted spin ensemble in a cavity: Inhomogeneous broadening as a stabilizing mechanism

We study the evolution of an inverted spin ensemble coupled to a cavity. The inversion itself presents an inherent instability of the system; however, the inhomogeneous broadening of spin-resonance frequencies presents a stabilizing mechanism, and a stability criterion is derived. The detailed behavior of mean values and variances of the spin components and of the cavity field is accounted for under both stable and unstable conditions.

quant-ph↗

arXiv2012

Effect of qubit losses on Grover's quantum search algorithm

We investigate the performance of Grover's quantum search algorithm on a register which is subject to loss of the particles that carry the qubit information. Under the assumption that the basic steps of the algorithm are applied correctly on the correspondingly shrinking register, we show that the algorithm converges to mixed states with 50% overlap with the target state in the bit positions still present. As an alternative to error correction, we present a procedure that combines the outcome of different trials of the algorithm to determine the solution to the full search problem. The procedure may be relevant for experiments where the algorithm is adapted as the loss of particles is registered, and for experiments with Rydberg blockade interactions among neutral atoms, where monitoring of the atom losses is not even necessary.

quant-ph↗

arXiv2012

Directional emission of single photons from small atomic samples

We provide a formalism to describe deterministic emission of single photons with tailored spatial and temporal profiles from a regular array of multi-level atoms. We assume that a single collective excitation is initially shared by all the atoms in a metastable atomic state, and that this state is coupled by a classical laser field to an optically excited state which rapidly decays to the ground atomic state. Our model accounts for the different field polarization components via re-absorption and emission of light by the Zeeman manifold of optically excited states.

quant-ph↗

arXiv2012

Squeezing of Collective Excitations in Spin Ensembles

We analyse the possibility to create two-mode spin squeezed states of two separate spin ensembles by inverting the spins in one ensemble and allowing spin exchange between the ensembles via a near resonant cavity field. We investigate the dynamics of the system using a combination of numerical and analytic calculations, and we obtain squeezing for a wide range of parameters. We also investigate the transfer of the squeezing properties to the cavity field and to an output mode from the cavity. Finally, we investigate how the squeezing is affected by effects of inhomogeneities which would be present in solid state implementations of the spin ensembles.

quant-ph↗

arXiv2012

Born-Oppenheimer description of two atoms in a combined oscillator and lattice trap

We analyze the quantum states of two atoms in a combined harmonic oscillator and periodic lattice trap in one spatial dimension. In the case of tight-binding and only nearest neighbor tunneling, the equations of motion are conveniently represented in the momentum representation. We show that in the case of strong attraction between the particles, the different time scales of relative and center-of-mass motion validate a separation of the problem similar to the Born-Oppenheimer approximation applied in the description of electronic and nuclear motion in molecules.

cond-mat.quant-gas↗

arXiv2012

Manipulation of qubits in non-orthogonal collective storage modes

We present an analysis of transfer of quantum information between the collective spin degrees of freedom of a large ensemble of two-level systems and a single central qubit. The coupling between the central qubit and the individual ensemble members may be varied and thus provides access to more than a single storage mode. Means to store and manipulate several independent qubits are derived for the case where the variation in coupling strengths does not allow addressing of orthogonal modes of the ensemble. While our procedures and analysis may apply to a number of different physical systems, for concreteness, we study the transfer of quantum states between a single electron spin and an ensemble of nuclear spins in a quantum dot.

quant-ph↗

arXiv2012

Spin squeezing and Schrödinger cat generation in atomic samples with Rydberg blockade

A scheme is proposed to prepare squeezed states and Schrödinger cat-like states of the collective spin degrees of freedom associated with a pair of ground states in an atomic ensemble. The scheme uses an effective Jaynes-Cummings interaction which can be provided by excitation of the atoms to Rydberg states and an effective J_x interaction implemented by a resonant Raman coupling between the atomic ground states. Both dynamical evolution with a constant Hamiltonian and with adiabatic variation of the two interaction terms are studied. We show that by the application of further resonant laser fields, we can suppress non-adiabatic transfer under the time varying Hamiltonian and significantly speed up the evolution towards a maximally squeezed, J_z=0, collective spin state.

quant-ph↗

arXiv2012

Relative and center-of-mass motion in the attractive Bose-Hubbard model

We present first-principle numerical calculations for few particle solutions of the attractive Bose-Hubbard model with periodic boundary conditions. We show that the low-energy many-body states found by numerical diagonalization can be written as translational superposition states of compact composite systems of particles. These compact states break the translational symmetry of the problem and their center-of-mass and internal excitations offer simple explanations of the energy spectrum of the full model.

cond-mat.quant-gas↗

arXiv2012

Interacting spins in a cavity: finite size effects and symmetry-breaking dynamics

We calculate the ground state and simulate the dynamics of a finite chain of spins with Ising nearest-neighbor interactions and a Dicke collective spin interaction with a single mode cavity field. We recover the signatures of first and second order phase transitions predicted by mean field theory, while for small chains, we find significant and non-trivial finite size effects. Below the first order phase transition, even quite large spin chains of 30-40 spins give rise to a mean photon number and number fluctuations significantly above the mean field vacuum result. Near the second order phase critical point, our calculations reveal photon number fluctuations that grow beyond Poisson statistics with the size of the spin chain. We simulate the stochastic evolution of the system when the cavity output field is subject to homodyne detection. For an initial state close to the first order phase-transition the random character of the measurement process causes a measurement-induced symmetry-breaking in the system. This symmetry-breaking occurs on the time-scale needed for an observer to gather sufficient information to distinguish between the two possible (mean-field) symmetry-broken states.

quant-ph↗

arXiv2012

Measurement-induced two-qubit entanglement in a bad cavity: Fundamental and practical considerations

An entanglement-generating protocol is described for two qubits coupled to a cavity field in the bad-cavity limit. By measuring the amplitude of a field transmitted through the cavity, an entangled spin-singlet state can be established probabilistically. Both fundamental limitations and practical measurement schemes are discussed, and the influence of dissipative processes and inhomogeneities in the qubits are analyzed. The measurement-based protocol provides criteria for selecting states with an infidelity scaling linearly with the qubit-decoherence rate.

quant-ph↗

arXiv2012

Qubit purification speed-up for three complementary continuous measurements

We consider qubit purification under simultaneous continuous measurement of the three non-commuting qubit operators σ_x, σ_y, σ_z. The purification dynamics is quantified by (i) the average purification rate, and (ii) the mean time of reaching given level of purity, (1-ε). Under ideal measurements (detector efficiency η=1), we show in the first case an asymptotic mean purification speed-up of 4 as compared to a standard (classical) single-detector measurement. However by the second measure --- the mean time of first passage T(ε) of the purity --- the corresponding speed-up is only 2. We explain these speed-ups using the isotropy of the qubit evolution that provides an equivalence between the original measurement directions and three simultaneous measurements, one with an axis aligned along the Bloch vector and the other with axes in the two complementary directions. For inefficient detectors, η=1-δ<1 the mean time of first passage T(δ,ε) increases since qubit purification competes with an isotropic qubit dephasing. In the asymptotic high-purity limit (ε, δ<< 1) we show that the increase possesses a scaling behavior: ΔT(δ,ε) is a function only of the ratio δ/ε. The increase ΔT(δ/ε) is linear for small argument but becomes exponential ~ exp(δ/2ε) for δ/ε large.

quant-ph↗

arXiv2011

Reflectivity and transmissivity of an optical cavity coupled to two-level atoms: Coherence properties and the influence of atomic phase noise

We consider N identical two-level atoms coupled to an optical cavity, which is coherently driven by an external field. In the limit of small atomic excitation, the reflection and transmission coefficients for both fields and intensities are calculated analytically. In addition, the frequency content of the cavity field and hence also the emission spectrum of the cavity is determined. It is discussed in particular how individual collisional dephasing and common atomic energy-level fluctuations prevent the cavity field from being in a coherent state, which in turn affects the outgoing fields.

quant-ph↗

arXiv2011

A quantum computation architecture using optical tweezers

We present a complete architecture for scalable quantum computation with ultracold atoms in optical lattices using optical tweezers focused to the size of a lattice spacing. We discuss three different two-qubit gates based on local collisional interactions. The gates between arbitrary qubits require the transport of atoms to neighboring sites. We numerically optimize the non-adiabatic transport of the atoms through the lattice and the intensity ramps of the optical tweezer in order to maximize the gate fidelities. We find overall gate times of a few 100 us, while keeping the error probability due to vibrational excitations and spontaneous scattering below 10^3. The requirements on the positioning error and intensity noise of the optical tweezer and the magnetic field stability are analyzed and we show that atoms in optical lattices could meet the requirements for fault-tolerant scalable quantum computing.

quant-ph↗

arXiv2011

Dynamics of the collective modes of an inhomogeneous spin ensemble in a cavity

We study the excitation dynamics of an inhomogeneously broadened spin ensemble coupled to a single cavity mode. The collective excitations of the spin ensemble can be described in terms of generalized spin waves and, in the absence of the cavity, the free evolution of the spin ensemble can be described as a drift in the wave number without dispersion. In this article we show that the dynamics in the presence of coupling to the cavity mode can be described solely by a modified time evolution of the wave numbers. In particular, we show that collective excitations with a well- defined wave number pass without dispersion from negative to positive valued wave numbers without populating the zero wave number spin wave mode. The results are relevant for multi-mode collective quantum memories where qubits are encoded in different spin waves.

quant-ph↗