arXiv subjects

Klaus Mølmer

Publications and source records attributed to Klaus Mølmer.

196 records · Page 11Linked to original sources

arXiv2011

Phase transitions in an Ising chain interacting with a single mode cavity field

We investigate the thermodynamics of a combined Dicke- and Ising-model which exhibits a rich phenomenology arising from the second order and quantum phase transitions from the respective models. The partition function is calculated using mean field theory, and the free energy is analyzed in detail to determine the complete phase diagram for the system. The analysis reveals both first- and second-order Dicke phase transitions into a super-radiant state, and the cavity mean-field in this regime acts as an effective magnetic field, which restricts the Ising chain dynamics to parameter ranges away from the Ising phase transition. Physical systems with a first order phase transitions are natural candidates for metrology and calibration purposes, and we apply filter theory to show that the sensitivity of the physical system to temperature and external fields reaches the 1/N Heisenberg limit.

quant-ph↗

arXiv2010

Topological matter with collective encoding and Rydberg blockade

We propose to use a permutation symmetric sample of multi-level atoms to simulate the properties of topologically ordered states. The Rydberg blockade interaction is used to prepare states of the sample which are equivalent to resonating valence bond states, Laughlin states, and string-net condensates and to create and study the properties of their quasi-particle-like fundamental excitations.

quant-ph↗

arXiv2010

Storage of multiple coherent microwave excitations in an electron spin ensemble

Electron and nuclear spins have good coherence times and an ensemble of spins is a promising candidate for a quantum memory. By employing holographic techniques via field gradients a single ensemble may be used to store many bits of information. Here we present a coherent memory using a pulsed magnetic field gradient, and demonstrate the storage and retrieval of up to 100 weak 10 GHz coherent excitations in collective states of an electron spin ensemble. We further show that such collective excitations in the electron spin can then be stored in nuclear spin states, which offer coherence times in excess of seconds.

quant-ph↗

arXiv2010

Qubit state monitoring by measurement of three complementary observables

We consider the evolution of a spin 1/2 (qubit) under the simultaneous continuous measurement of three non-commuting qubit operators sigma_x, sigma_y, sigma_z. For identical ideal detectors the qubit state evolves by approaching a pure state with a random direction in the Bloch vector space and by undergoing locally isotropic diffusion in the perpendicular directions. The quantum state conditioned on the complete detector record is used to assess the fidelity of classically inspired estimates based on running time averages and discrete time bin detector outputs.

quant-ph↗

arXiv2010

Deterministic multi-mode photonic device for quantum information processing

We propose the implementation of a light source, which can deterministically generate a rich variety of multi-mode quantum states. The desired states are encoded in the collective population of different ground hyperfine states of an atomic ensemble and converted to multi-mode photonic states by excitation to optically excited levels followed by cooperative spontaneous emission. Among our examples of applications, we demonstrate how two-photon entangled states can be prepared and implemented in a protocol for reference frame free quantum key distribution and how one-dimensional as well as higher-dimensional cluster states can be produced.

quant-ph↗

arXiv2010

Analyzing quantum jumps of one and two atoms strongly coupled to an optical cavity

We induce quantum jumps between the hyperfine ground states of one and two Cesium atoms, strongly coupled to the mode of a high-finesse optical resonator, and analyze the resulting random telegraph signals. We identify experimental parameters to deduce the atomic spin state nondestructively from the stream of photons transmitted through the cavity, achieving a compromise between a good signal-to-noise ratio and minimal measurement-induced perturbations. In order to extract optimum information about the spin dynamics from the photon count signal, a Bayesian update formalism is employed, which yields time-dependent probabilities for the atoms to be in either hyperfine state. We discuss the effect of super-Poissonian photon number distributions caused by atomic motion.

quant-ph↗

arXiv2009

Simulating local measurements on a quantum many body system with stochastic matrix product states

We demonstrate how to simulate both discrete and continuous stochastic evolution of a quantum many body system subject to measurements using matrix product states. A particular, but generally applicable, measurement model is analyzed and a simple representation in terms of matrix product operators is found. The technique is exemplified by numerical simulations of the anti-ferromagnetic Heisenberg spin-chain model subject to various instances of the measurement model. In particular we focus on local measurements with small support and non-local measurements which induces long range correlations.

quant-ph↗

arXiv2009

Weak measurements with a qubit meter

We derive schemes to measure the so-called weak values of quantum system observables by coupling of the system to a qubit meter system. We highlight, in particular, the meaning of the imaginary part of the weak values, and show how it can be measured directly on equal footing with the real part of the weak value. We present compact expressions for the weak value of single qubit observables and of product observables on qubit pairs. Experimental studies of the results are suggested with cold trapped ions.

quant-ph↗

arXiv2009

Correlations in local measurements on a quantum state, and complementarity as an explanation of nonclassicality

We consider the classical correlations that two observers can extract by measurements on a bipartite quantum state, and we discuss how they are related to the quantum mutual information of the state. We show with several examples how complementarity gives rise to a gap between the quantum and the classical correlations, and we relate our quantitative finding to the so-called classical correlation locked in a quantum state. We derive upper bounds for the sum of classical correlation obtained by measurements in different mutually unbiased bases and we show that the complementarity gap is also present in the deterministic quantum computation with one quantum bit.

quant-ph↗

arXiv2009

Entropic uncertainty relation for mutually unbiased bases

We derive new inequalities for the probabilities of projective measurements in mutually unbiased bases of a qudit system. These inequalities lead to wider ranges of validity and tighter bounds on entropic uncertainty inequalities previously derived in the literature.

quant-ph↗

arXiv2009

Complementarity of information sent via different bases

We discuss quantitatively the complementarity of information transmitted by a quantum system prepared in a basis state in one out of several different mutually unbiased bases (MUBs). We obtain upper bounds on the information available to a receiver who has no knowledge of which MUB was chosen by the sender. These upper bounds imply a complementarity of information encoded via different MUBs and ultimately ensure the security in quantum key distribution protocols.

quant-ph↗

arXiv2007

Quantum state reconstruction with imperfect rotations on an inhomogeneously broadened ensemble of qubits

We present a method for performing quantum state reconstruction on qubits and qubit registers in the presence of decoherence and inhomogeneous broadening. The method assumes only rudimentary single qubit rotations as well as knowledge of decoherence and loss mechanisms. We show that full state reconstruction is possible even in the case where single qubit rotations may only be performed imperfectly. Furthermore we show that for ensemble quantum computing proposals, quantum state reconstruction is possible even if the ensemble experiences inhomogeneous broadening and if only imperfect qubit manipulations are available during state preparation and reconstruction.

quant-ph↗

arXiv2006

Effects of ground state hyperfine shifts in quantum computing with optically hole burnt materials

We present an investigation of the effects of constant but random shifts of the ground hyperfine qubit states in the setting of quantum computing with ion doped crystals. Complex hyperbolic secant pulses can be used to transfer ions reliably to electronically excited states, and a perturbative approach is used to analyse the effect of ground state hyperfine shifts. This analysis shows that the errors due to the hyperfine shift are dynamically supressed during gate operation, a fact we attribute to the AC Stark shift. Furthermore we present an implementation of a controlled phase gate which is resilient to the effects of the hyperfine shift. Decoherence and decay effects are included in simulations in order to show that a demonstration of quantum gates is feasible over the relevant range of system parameters.

quant-ph↗

arXiv2005

Phase-matched four wave mixing and quantum beam splitting of matter waves in a periodic potential

We show that the dispersion properties imposed by an external periodic potential ensure both energy and quasi-momentum conservation such that correlated pairs of atoms can be generated by four wave mixing from a Bose-Einstein condensate moving in an optical lattice potential. In our numerical solution of the Gross-Pitaevskii equation, a condensate with initial quasi-momentum k_0 is transferred almost completely (>95%) into a pair of correlated atomic components with quasi-momenta k_1 and k_2, if the system is seeded with a smaller number of atoms with the appropriate quasi-momentum k_1.

cond-mat.other↗

arXiv2004

Spin squeezing and precision probing with light and samples of atoms in the gaussian approximation

We consider an ensemble of trapped atoms interacting with a continuous wave laser field. For sufficiently polarized atoms and for a polarized light field, we may approximate the non-classical components of the collective spin angular momentum operator for the atoms and the Stokes vectors of the field by effective position and momentum variables for which we assume a gaussian state. Within this approximation, we present a theory for the squeezing of the atomic spin by polarization rotation measurements on the probe light. We derive analytical expressions for the squeezing with and without inclusion of the noise effects introduced by atomic decay and by photon absorption. The theory is readily adapted to the case of inhomogeneous light-atom coupling [A. Kuzmich and T.A.B. Kennedy, Phys. Rev. Lett. Vol. 92, 030407 (2004)]. As a special case, we show how to formulate the theory for an optically thick sample by slicing the gas into pieces each having only small photon absorption probability. Our analysis of a realistic probing and measurement scheme shows that it is the maximally squeezed component of the atomic gas that determines the accuracy of the measurement.

quant-ph↗

arXiv2004

Number distributions for fermions and fermionized bosons in periodic potentials

We compute the spatial population statistics for one-dimensional fermi-gases and for bose-gases with hard core repulsions in periodic potentials. We show how the statistics depend on the atomic density in the ground state of the system, and we present calculations for the dynamical turn-on of the potential.

cond-mat.soft↗