arXiv subjects

M. K. Olsen

Publications and source records attributed to M. K. Olsen.

At least 55 records · Page 3Linked to original sources

arXiv2011

Generalised purity as an entanglement measure for two- and three-well Bose-Hubbard models

The SU(2) and SU(3) Lie algebras lend themselves naturally to studies of two- and three-well Bose-Einstein condensates, with the group operators being expressed in terms of bosonic annihilation and creation operators at each site. The success of these representations has led to the purities associated with these algebras to be promoted as a measure of entanglement between the atomic modes in each well. In this report, we show that these purities do not provide an unambiguous measure, but instead give results which depend on the quantum statistical states of each atomic mode. Using the example of totally uncoupled modes which have never interacted, we quantify these purities for different states and show that completely separable states can give values which have been claimed to indicate the presence of entanglement.

quant-ph↗

arXiv2011

Quantum dynamics of a four-well Bose-Hubbard model with two different tunneling rates

We consider a theoretical model of a four-mode Bose-Hubbard model consisting of two pairs of wells coupled via two processes with two different rates. The model is naturally divided into two subsystems with strong intra-system coupling and much weaker coupling between the two subsystems and has previously been introduced as a model for Josephson heat oscillations by Strzys and Anglin [\pra {\bf 81}, 043616 (2010) ]. We examine the quantum dynamics of this model for a range of different initial conditions, in terms of both the number distribution among the wells and the quantum statistics. We find that the time evolution is different to that predicted by a mean-field model and that this system exhibits a wide range of interesting behaviours. We find that the system equilibriates to a maximum entropy state and is thus a useful model for quantum thermalisation. As our model may be realised to a good approximation in the laboratory, it becomes a candidate for experimental investigation.

quant-ph↗

arXiv2010

Analysis of a continuous-variable quadripartite cluster state from a single optical parametric oscillator

We examine the feasibility of generating continuous-variable multipartite entanglement in an intra-cavity quadruply concurrent downconversion scheme that has been proposed for the generation of cluster states by Menicucci \textit{et al.} [Physical Review Letters \textbf{101}, 130501 (2008)]. By calculating optimized versions of the van Loock-Furusawa correlations we demonstrate genuine quadripartite entanglement and investigate the degree of entanglement present. Above the oscillation threshold the basic cluster state geometry under consideration suffers from phase diffusion. We alleviate this problem by incorporating a small injected signal into our analysis. Finally, we investigate squeezed joint operators. While the squeezed joint operators approach zero in the undepleted regime, we find that this is not the case when we consider the full interaction Hamiltonian and the presence of a cavity. In fact, we find that the decay of these operators is minimal in a cavity, and even depletion alone inhibits cluster state formation.

quant-ph↗

arXiv2010

Asymmetric Gaussian steering: when Alice and Bob disagree

Asymmetric steering is an effect whereby an inseparable bipartite system can be found to be described by either quantum mechanics or local hidden variable theories depending on which one of Alice or Bob makes the required measurements. We show that, even with an inseparable bipartite system, situations can arise where Gaussian measurements on one half are not sufficient to answer the fundamental question of which theory gives an adequate description and the whole system must be considered. This phenomenon is possible because of an asymmetry in the definition of the original Einstein-Podolsky-Rosen paradox and in this article we show theoretically that it may be demonstrated, at least in the case where Alice and Bob can only make Gaussian measurements, using the intracavity nonlinear coupler.

quant-ph↗

arXiv2010

Quadripartite continuous-variable entanglement via quadruply concurrent downconversion

We investigate an intra-cavity coupled down-conversion scheme to generate quadripartite entanglement using concurrently resonant nonlinearities. We verify that quadripartite entanglement is present in this system by calculating the output fluctuation spectra and then considering violations of optimized inequalities of the van Loock-Furusawa type. The entanglement characteristics both above and below the oscillation threshold are considered. We also present analytic solutions for the quadrature operators and the van Loock-Furusawa correlations in the undepleted pump approximation.

quant-ph↗

arXiv2009

Demonstrating mesoscopic superpositions in double-well Bose-Einstein condensates

The availability of Bose-Einstein condensates as mesoscopic or macroscopic quantum objects has aroused new interest in the possiblity of making and detecting coherent superpositions involving many atoms. In this article we show that it may be possible to generate such a superposition state in a reasonably short time using Feshbach resonances to tune the inter-atomic interactions in a double-well condensate. We also consider the important problem of distinguishing whether a coherent superposition or a statistical mixture is generated by a given experimental procedure. We find that unambiguously distinguishing even a perfect `NOON' state from a statistical mixture using standard detection methods will present experimental difficulties.

quant-ph↗

arXiv2009

Numerical representation of quantum states in the positive-P and Wigner representations

Numerical stochastic integration is a powerful tool for the investigation of quantum dynamics in interacting many body systems. As with all numerical integration of differential equations, the initial conditions of the system being investigated must be specified. With application to quantum optics in mind, we show how various commonly considered quantum states can be numerically simulated by the use of widely available Gaussian and uniform random number generators. We note that the same methods can also be applied to computational studies of Bose-Einstein condensates, and give some examples of how this can be done.

cond-mat.quant-gas↗

arXiv2009

Commuting Heisenberg operators as the quantum response problem: Time-normal averages in the truncated Wigner representation

The applicability of the so-called truncated Wigner approximation (-W) is extended to multitime averages of Heisenberg field operators. This task splits naturally in two. Firstly, what class of multitime averages the -W approximates, and, secondly, how to proceed if the average in question does not belong to this class. To answer the first question we develop an (in principle, exact) path-integral approach in phase-space based on the symmetric (Weyl) ordering of creation and annihilation operators. These techniques calculate a new class of averages which we call time-symmetric. The -W equations emerge as an approximation within this path-integral techniques. We then show that the answer to the second question is associated with response properties of the system. In fact, for two-time averages Kubo's renowned formula relating the linear response function to two-time commutators suffices. The -W is trivially generalised to the response properties of the system allowing one to calculate approximate time-normally ordered two-time correlation functions with surprising ease. The techniques we develop are demonstrated for the Bose-Hubbard model.

cond-mat.stat-mech↗

arXiv2009

A comparative study of dynamical simulation methods for the dissociation of molecular Bose-Einstein condensates

We describe a pairing mean-field theory related to the Hartree-Fock-Bogoliubov approach, and apply it to the dynamics of dissociation of a molecular Bose-Einstein condensate (BEC) into correlated bosonic atom pairs. We also perform the same simulation using two stochastic phase-space techniques for quantum dynamics -- the positive P-representation method and the truncated Wigner method. By comparing the results of our calculations we are able to assess the relative strength of these theoretical techniques in describing molecular dissociation in one spatial dimension. An important aspect of our analysis is the inclusion of atom-atom interactions which can be problematic for the positive-P method. We find that the truncated Wigner method mostly agrees with the positive-P simulations, but can be simulated for significantly longer times. The pairing mean-field theory results diverge from the quantum dynamical methods after relatively short times.

quant-ph↗

arXiv2009

Detection of continuous variable entanglement without coherent local oscillators

We propose three criteria for identifying continuous variable entanglement between two many-particle systems with no restrictions on the quantum state of the local oscillators used in the measurements. Mistakenly asserting a coherent state for the local oscillator can lead to incorrectly identifying the presence of entanglement. We demonstrate this in simulations with 100 particles, and also find that large number fluctuations do not prevent the observation of entanglement. Our results are important for quantum information experiments with realistic Bose-Einstein condensates or in optics with arbitrary photon states.

quant-ph↗

arXiv2007

Bright bichromatic entanglement and quantum dynamics of sum frequency generation

We investigate the quantum properties of the well-known process of sum frequency generation, showing that it is potentially a very useful source of non-classical states of the electromagnetic field, some of which are not possible with the more common techniques. We show that it can produce quadrature squeezed light, bright bichromatic entangled states and symmetric and asymmetric demonstrations of the Einstein-Podolsky-Rosen paradox. We also show that the semiclassical equations totally fail to describe the mean-field dynamics when the cavity is strongly pumped.

quant-ph↗

arXiv2007

Pairing mean-field theory for the dynamics of dissociation of molecular Bose-Einstein condensates

We develop a pairing mean-field theory to describe the quantum dynamics of the dissociation of molecular Bose-Einstein condensates into their constituent bosonic or fermionic atoms. We apply the theory to one, two, and three-dimensional geometries and analyze the role of dimensionality on the atom production rate as a function of the dissociation energy. As well as determining the populations and coherences of the atoms, we calculate the correlations that exist between atoms of opposite momenta, including the column density correlations in 3D systems. We compare the results with those of the undepleted molecular field approximation and argue that the latter is most reliable in fermionic systems and in lower dimensions. In the bosonic case we compare the pairing mean-field results with exact calculations using the positive-$P$ stochastic method and estimate the range of validity of the pairing mean-field theory. Comparisons with similar first-principle simulations in the fermionic case are currently not available, however, we argue that the range of validity of the present approach should be broader for fermions than for bosons in the regime where Pauli blocking prevents complete depletion of the molecular condensate.

cond-mat.other↗

arXiv2007

Bright continuous-variable entanglement from the quantum optical dimer

We show theoretically that two evanescently coupled $χ^{(2)}$ second harmonic generators inside a Fabry-Perot cavity provide a tunable source of quadrature squeezed light, Einstein-Podolsky-Rosen correlations and quantum entanglement. Unlike systems using coupled downconverters, second harmonic generation has no oscillation threshhold, so that the entangled fields become macroscopically occupied as soon as the pumping fields are turned on. This system also gives two frequencies at which the entangled fields can have macroscopic intensity. We show how the entanglement properties can be controlled by adjusting the pumping, the coupling strengths and the cavity detunings.

quant-ph↗

arXiv2007

Tripartite entanglement and threshold properties of coupled intracavity downconversion and sum-frequency generation

The process of cascaded downconversion and sum-frequency generation inside an optical cavity has been predicted to be a potential source of three-mode continuous-variable entanglement. When the cavity is pumped by two fields, the threshold properties have been analysed, showing that these are more complicated than in well-known processes such as optical parametric oscillation. When there is only a single pumping field, the entanglement properties have been calculated using a linearised fluctuation analysis, but without any consideration of the threshold properties or critical operating points of the system. In this work we extend this analysis to demonstrate that the singly pumped system demonstrates a rich range of threshold behaviour when quantisation of the pump field is taken into account and that asymmetric polychromatic entanglement is available over a wide range of operational parameters.

quant-ph↗

arXiv2007

Quantum statistical measurements of an atom laser beam

We describe a scheme, operating in a manner analogous to a reversed Raman output coupler, for measuring the phase-sensitive quadrature statistics of an atom laser beam. This scheme allows for the transferral of the atomic field statistics to an optical field, for which the quantum statistics may then be measured using the well-developed technology of optical homodyne measurement.

physics.atom-ph↗

arXiv2007

Teleportation of massive particles without shared entanglement

We propose a method for quantum state transfer from one atom laser beam to another via an intermediate optical field, using Raman incoupling and outcoupling techniques. Our proposal utilises existing experimental technologies to teleport macroscopic matter waves over potentially large distances without shared entanglement.

quant-ph↗

arXiv2006

Measuring the quantum statistics of an atom laser beam

We propose and analyse a scheme for measuring the quadrature statistics of an atom laser beam using extant optical homodyning and Raman atom laser techniques. Reversal of the normal Raman atom laser outcoupling scheme is used to map the quantum statistics of an incoupled beam to an optical probe beam. A multimode model of the spatial propagation dynamics shows that the Raman incoupler gives a clear signal of de Broglie wave quadrature squeezing for both pulsed and continuous inputs. Finally, we show that experimental realisations of the scheme may be tested with existing methods via measurements of Glauber's intensity correlation function.

quant-ph↗

arXiv2006

Tripartite entanglement from interlinked $χ^{(2)}$ parametric interactions

We examine the tripartite entanglement properties of an optical system using interlinked $χ^{(2)}$ interactions, recently studied experimentally in terms of its phase-matching properties by Bondani et al [M. Bondani, A. Allevi, E. Gevinti, A. Agliati, and A. Andreoni, arXiv:quant-ph/0604002.]. We show that the system does produce output modes which are genuinely tripartite entangled and that detection of this entanglement depends crucially on the correlation functions which are measured, with a three-mode Einstein-Podolsky-Rosen inequality being the most sensitive.

quant-ph↗