arXiv subjects

M. K. Olsen

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

At least 37 records · Page 2Linked to original sources

arXiv2016

Negative differential conductivity and quantum statistical effects in a three-site Bose-Hubbard model

The use of an electron beam to remove ultracold atoms from selected sites in an optical lattice has opened up new opportunities to study transport in quantum systems [R. Labouvie {\it et al.\ }, Phys.\ Rev.\ Lett.\ {\bf 115}, 050601 (2015)]. Inspired by this experimental result, we examine the effects of number difference, dephasing, and initial quantum statistics on the filling of an initially depleted middle well in the three-well inline Bose-Hubbard model. We find that the well-known phenomenon of macroscopic self-trapping is the main contributor to oscillatory negative differential conductivity in our model, with phase diffusion being a secondary effect. However, we find that phase diffusion is required for the production of direct atomic current, with the coherent process showing damped oscillatory currents. We also find that our results are highly dependent on the initial quantum states of the atoms in the system.

cond-mat.quant-gas↗

arXiv2016

Two-well atomic Bose-Hubbard analogues of optical cavities

We propose and analyse analogs of optical cavities for atoms using two-well Bose-Hubbard models with pumping and losses. With one well pumped, we find that both the mean-field dynamics and the quantum statistics show a quantitative dependence on the choice of damped well. Both the systems we analyse remain far from equilibrium, preserving good coherence between the wells in the steady-state. We find a small degree of quadrature squeezing and mode entanglement for some parameter regimes. Due to recent experimental advances, it should be possible to demonstrate the effects we investigate and predict.

quant-ph↗

arXiv2016

Comment on "Negative Differential Conductivity in an Interacting Quantum Gas."

Labouvie \etal (\prl {\bf 115}, 050601, (20015)) recently demonstrated negative differential conductivity (NDC) in a multi-well Bose-Einstein condensate. They stated "we demonstrate that NDC originates from a nonlinear, atom number dependent tunneling coupling in combination with fast collisional decoherence." We show theoretically how the essential feature of NDC, a reduction in atomic current caused by an increase in chemical potential, is present in unitary dynamics through the well-known mechanism of macroscopic self-trapping (MST), and that the collisional decoherence merely serves as a quantitative modification of this.

cond-mat.quant-gas↗

arXiv2015

Tripartite and bipartite entanglement in continuous-variable tripartite systems

We examine one asymmetric adnd two fully symmetric Gaussian continuous-variable systems in terms of their tripartite and bipartite entanglement properties. We treat pure states and are able to find analytic solutions using the undepleted pump approximation for the Hamiltonian models, and standard beamsplitter relations for a model that mixes the outputs of optical parametric oscillators. Our two symmetric systems exhibit perfect tripartite correlations, but only in the unphysical limit of infinite squeezing. For more realistic squeezing parameters, all three systems exhibit both tripartite and bipartite entanglement. We conclude that none of the outputs are completely analogous to either GHZ or W states, but there are parameter regions where they produce T states introduced by Adesso \etal The qualitative differences in the output states for different interaction parameters indicate that continuous-variable tripartite quantum information systems offer a versatility not found in bipartite systems.

quant-ph↗

arXiv2015

Entanglement via a three-well Bose-Hubbard system and via an optical beamsplitter

We compare and contrast the entangling properties of a three-well Bose-Hubbard model and an optical beamsplitter. The coupling between the different modes is linear in both cases, and we may identify two output modes. Obvious differences are that our Bose-Hubbard model, with only the middle well initially occupied, does not have a vacuum input port, there is no equivalent of a collisional, $χ^{(3)}$ nonlinearity with the beamsplitter, and the results of the Bose-Hubbard model show a time-dependence. In the non-interacting case, we obtain analytic solutions and show that, like a beamsplitter, the Bose-Hubbard system will not produce entanglement for classical initial states. We also show that whether inseparability or entanglement are detected depends sensitively on the criteria measured, with different criteria giving contradictory predictions.

quant-ph↗

arXiv2015

A critical evaluation of bipartite entanglement and steering measures in a genuinely tripartite entangled system

A large number of inequalities have been proposed for the detection of bipartite continuous variable entanglement and Einstein-Podolsky-Rosen steering. Many of these are based on either measured or inferred variances and are relatively easily measured via homodyne detection of optical outputs. In this work we examine a number of bipartite inequalities in the process of cascaded downconversion and sum-frequency generation inside an optical cavity. This has previously been predicted to be a potential source of continuous-variable tripartite entanglement, therefore we know that there are no separable bipartitions. In this work we investigate the performance of the chosen inequalities in the stable, below threshold regime. We show that detection of the existing entanglement is sensitive to the actual inequalities chosen, with some criteria missing it completely. Our results are explained by the fact that violation of the chosen inequalities is sufficient but not necessary to demonstrate the non-classical relationships between the modes, and highlights the outstanding problem of developing a reliable continuous-variable entanglement measure.

quant-ph↗

arXiv2015

Spreading of entanglement and steering along small Bose-Hubbard chains

We investigate how entanglement spreads along small Bose-Hubbard chains, with only the first well initially occupied by a mesoscopic number of atoms, as the number of sites increases. For two- and three-well chains in the non-interacting case, we are able to obtain analytical solutions and show that the presence of entanglement depends on having a sub-Poissonian state of the atoms in the first well. In these cases, the correlations we calculate are completely periodic. Restoring the collisional interactions or moving to a four-well chain necessitates a numerical treatment, for which we use the fully quantum positive-P representation. We examine two different correlations and find that adding collisional interactions destroys the periodicity of the correlations and causes them to degrade with time. This happens well before there is a noticeable effect on the periodicity of the solutions for the number of atoms in each well.

quant-ph↗

arXiv2015

An entangling atomtronic beamsplitter

We propose and analyse the use of a three-well Bose-Hubbard model for the creation of two spatially separated entangled atomic samples. Our three wells are in a linear configuration, with all atoms initially in the middle well, which gives some spatial separation of the two end wells. The evolution from the initial quantum state allows for the development of entanglement between the atomic modes in the two end wells. Using inseparability criteria developed by Hillery and Zubairy, we show how the detected entanglement is time dependent, oscillating with the well occupations. We suggest and analyse a method for preserving the entanglement by turning off the different interactions when it reaches its first maximum. We analyse the system with both Fock and coherent initial states, showing that the violations of the Hillery-Zubairy inequality exist only for initial Fock states and that the collisional nonlinearity degrades them. This system is an early step towards producing entangled atomic samples that can be spatially separated and thus close the locality loophole in tests of non-local quantum correlations.

quant-ph↗

arXiv2015

Quantum ultra-cold atomtronics

It is known that a semi-classical analysis is not always adequate for atomtronics devices, but that a fully quantum analysis is often necessary to make reliable predictions. While small numbers of atoms at a small number of sites are tractable using the density matrix, a fully quantum analysis is often not straightforward as the system becomes larger. We show that the fully quantum positive-P representation is then a viable calculational tool. We postulate an atomtronic phase-gate consisting of four wells in a Bose-Hubbard configuration, for which the semi-classical dynamics are controllable using the phase of the atomic mode in one of the wells. We show that the quantum predictions of the positive-P representation for the performance of this device have little relation to those found semi-classically, and that the performance depends markedly on the actual quantum states of the initially occupied modes. We find that initial coherent states lead to closest to classical dynamics, but that initial Fock states give results that are quite different. A fully quantum analysis also opens the door for deeply quantum atomtronics, in which properties such as entanglement and EPR (Einstein-Podolsky-Rosen) steering become valuable technical properties of a device.

quant-ph↗

arXiv2015

Non-Gaussian pure states and positive Wigner functions

Non-Gaussian correlations in a pure state are inextricably linked with non-classical features, such as a non positive-definite Wigner function. In a commonly used simulation technique in ultracold atoms and quantum optics, known as the truncated Wigner method, the quantum dynamics is mapped to stochastic trajectories in phase space, governed by a positive approximation to the true Wigner distribution. The question thus arises: how accurate is this approach in predicting truly non-classical behaviour? In this article, we benchmark the ability of the truncated Wigner phase-space method to reproduce the non-Gaussian statistics of the single mode anharmonic oscillator. We find that the this method can reliably predict departures from Gaussian statistics over a wide range of particle numbers, whereas the positive-P representation method, which is in principle exact, can suffer from divergent instabilities. The truncated Wigner function, furthermore, is able to reproduce the non-Gaussian correlations while satisfying the condition for purity.

quant-ph↗

arXiv2014

Asymmetric steering in coherent transport of atomic population with a three-well Bose-Hubbard model

We analyse the Einstein-Podolsky-Rosen (EPR) steering properties in a three-well Bose-Hubbard model under the mechanism of coherent transport of atomic population (CTAP). This process, also known as transport without transit (TWT), transfers condensed atoms from one well of a lattice potential to another, non-adjacent well, without macroscopic occupation of the middle well. The dynamics and entanglement properties of this system have previously been analysed and shown to be dependent on the initial quantum state of the atoms in the first well. In this work we utilise the phase-space method of stochastic integration in the positive-P representation. The system demonstrated inseparability between the wells for Fock initial states, and we show that steering is also only found for an initial Fock state. Depending on how we write our steering inequalities, steering is seen at different times, showing a basic asymmetry. This means that for part of the evolution, Alice can steer Bob but not vice versa. After the midpoint of the population transfer, this situation reverses.

quant-ph↗

arXiv2014

Einstein-Podolsky-Rosen entanglement and steering in two-well BEC ground states

We consider how to generate and detect Einstein-Podolsky-Rosen (EPR) entanglement and the steering paradox between groups of atoms in two separated potential wells in a Bose-Einstein condensate (BEC). We present experimental criteria for this form of entanglement, and propose experimental strategies for detecting entanglement using two or four mode ground states. These approaches use spatial and/or internal modes. We also present higher order criteria that act as signatures to detect the multiparticle entanglement present in this system. We point out the difference between spatial entanglement using separated detectors, and other types of entanglement that do n}ot require spatial separation. The four-mode approach with two spatial and two internal modes results in an entanglement signature with spatially separated detectors, conceptually similar to the original EPR paradox.

quant-ph↗

arXiv2014

Quantum dynamics and entanglement in coherent transport of atomic population

In this work we look at the quantum dynamics of the process known as either transport without transit (TWT), or coherent transfer of atomic population (CTAP), of a Bose-Einstein condensate from one well of a lattice potential to another, non-adjacent well, without macroscopic occupation of the well between the two. This process has previously been analysed and in this work we extend those analyses by considering the effects of quantum statistics on the dynamics and entanglement properties of the condensate modes in the two relevant wells. In order to do this, we go beyond the mean-field analysis of the Gross-Pitaevskii type approach and utilise the phase-space stochastic methods so well known in quantum optics. In particular, we use the exact positive-P representation where it is suitable, and the approximate truncated WIgner representation otherwise. We find strong agreement between the results of these two methods, with the mean-field dynamics not depending on the initial quantum states of the trapped condensate. We find that the entanglement properties do depend strongly on the initial quantum states, with quantitatively different results found for coherent and Fock states. Comparison of the two methods gives us confidence that the truncated Wigner representation delivers accurate results for this system and is thus a useful method as the collisional nonlinearity increases and the positive-P results fail to converge.

quant-ph↗

arXiv2013

Asymmetric Gaussian harmonic steering in second harmonic generation

Intracavity second harmonic generation is one of the simplest of the quantum optical processes and is well within the expertise of most optical laboratories. It is well understood and characterised, both theoretically and experimentally. We show that it can be a source of continuous variable asymmetric Gaussian harmonic steering with fields which have a coherent excitation, hence combining the important effects of harmonic entanglement and asymmetric steering in one easily controllable device, adjustable by the simple means of tuning the cavity loss rates at the fundamental and harmonic frequencies. We find that whether quantum steering is available via the standard measurements of the Einstein-Podolsky-Rosen correlations can depend on which quadrature measurements are inferred from output spectral measurements of the fundamental and the harmonic. Altering the ratios of the cavity loss rates can be used to tune the regions where symmetric steering is available, with the results becoming asymmetric over all frequencies as the cavity damping at the fundamental frequency becomes significantly greater than at the harmonic. This asymmetry and its functional dependence on frequency is a potential new tool for experimental quantum information science, with possible utility for quantum key distribution. Although we show the effect here for Gaussian measurements of the quadratures, and cannot rule out a return of the steering symmetry for some class of non-Gaussian measurements, we note here that the system obeys Gaussian statistics in the operating regime investigated and Gaussian inference is at least as accurate as any other method for calculating the necessary correlations. Perhaps most importantly, this system is simpler than any other methods we are aware of which have been used or proposed to create asymmetric steering.

quant-ph↗

arXiv2013

Improved quantum correlations in second harmonic generation with a squeezed pump

We investigate the effects of a squeezed pump on the quantum properties and conversion efficiency of the light produced in single-pass second harmonic generation. Using stochastic integration of the two-mode equations of motion in the positive-P representation, we find that larger violations of continuous-variable harmonic entanglement criteria are available for lesser effective interaction strengths than with a coherent pump. This enhancement of the quantum properties also applies to violations of the Reid-Drummond inequalities used to demonstrate a harmonic version of the Einstein-Podolsky-Rosen paradox. We find that the conversion efficiency is largely unchanged except for very low pump intensities and high levels of squeezing.

quant-ph↗

arXiv2013

Non-Gaussian continuous-variable entanglement and steering

Two Kerr-squeezed optical beams can be combined in a beamsplitter to produce non-Gaussian continuous-variable entangled states. We characterize the non-Gaussian nature of the output by calculating the third-order cumulant of quadrature variables, and predict the level of entanglement that could be generated by evaluating the Duan-Simon and Reid Einstein-Podolsky-Rosen criteria. These states have the advantage over Gaussian states and non-Gaussian measurement schemes in that the well known, efficient and proven technology of homodyne detection may be used for their characterisation. A physical demonstration maintaining the important features of the model could be realised using two optical fibres, beamsplitters, and homodyne detection.

quant-ph↗

arXiv2011

Quantum phase-space analysis of population equilibration in multi-well ultracold atomic systems

We examine the medium time quantum dynamics and population equilibration of two, three and four-well Bose-Hubbard models using stochastic integration in the truncated Wigner phase-space representation. We find that all three systems will enter at least a temporary state of equilibrium, with the details depending on both the classical initial conditions and the initial quantum statistics. We find that classical integrability is not necessarily a good guide as to whether equilibration will occur. We construct an effective single-particle reduced density matrix for each of the systems, using the expectation values of operator moments, and use this to calculate an effective entropy. Knowing the expected maximum values of this entropy for each system, we are able to quantify the different approaches to equilibrium.

cond-mat.quant-gas↗

arXiv2011

Spectral Analysis of a Four Mode Cluster State

We theoretically evaluate the squeezed joint operators produced in a single optical parametric oscillator which generates quadripartite entangled outputs, as demonstrated experimentally by Pysher et al. \cite{pysher}[Phys. Rev. Lett. 107, 030505 (2011)]. Using a linearized fluctuation analysis we calculate the squeezing of the joint quadrature operators below threshold for a range of local oscillator phases and frequencies. These results add to the existing theoretical understanding of this potentially important system.

quant-ph↗