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M. K. Olsen

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

At least 19 recordsLinked to original sources
arXiv2019

Quantum chaos in a Bose-Hubbard dimer with modulated tunnelling

In the large-$N$, classical limit, the Bose-Hubbard dimer undergoes a transition to chaos when its tunnelling rate is modulated in time. We use exact and approximate numerical simulations to determine the features of the dynamically evolving state that are correlated with the presence of chaos in the classical limit. We propose the statistical distance between initially similar number distributions as a reliable measure to distinguish regular from chaotic behaviour in the quantum dynamics. Besides being experimentally accessible, number distributions can be efficiently reconstructed numerically from binned phase-space trajectories in a truncated Wigner approximation. Although the evolving Wigner function becomes very irregular in the chaotic regions, the truncated Wigner method is nevertheless able to capture accurately the beyond mean-field dynamics.

quant-ph↗
arXiv2017

Mesoscopic dynamical differences from quantum state preparation in a Bose-Hubbard trimer

Conventional wisdom is that quantum effects will tend to disappear as the number of quanta in a system increases, and the evolution of a system will become closer to that described by mean field classical equations. In this letter we combine newly developed experimental techniques to propose and analyse an experiment using a Bose-Hubbard trimer where the opposite is the case. We find that differences in the preparation of a centrally evacuated trimer can lead to readily observable differences in the subsequent dynamics which increase with system size. Importantly, these differences can be detected by the simple measurements of atomic number.

quant-ph↗
arXiv2017

Quantum correlations across two octaves from combined up and down conversion

We propose and analyse a cascaded optical parametric system which involves three interacting modes across two octaves of frequency difference. Our system, combining degenerate optical parametric oscillation (OPO) with second harmonic generation (SHG), promises to be a useful source of squeezed and entangled light at three differing frequencies. We show how changes in damping rates and the ratio of the two concurrent nonlinearities affect the quantum correlations in the output fields. We analyse the threshold behaviour, showing how the normal OPO threshold is changed by the addition of the SHG interactions. We also find that the inclusion of the OPO interaction removes the self-pulsing behaviour found in normal SHG. Finally, we show how the Einstein-Podolsky-Rosen correlations can be controlled by the injection of a coherent seed field at the lower frequency.

quant-ph↗
arXiv2017

Controlled asymmetry of EPR steering with an injected non-degenerate optical parametric oscillator

We propose and analyse a nonlinear optical apparatus in which the direction of asymmetric steering is controllable within the apparatus, rather than by adding noise to measurements. Using a nondegenerate parametric oscillator with an injected signal field, we show how the directionality and extent of the steering can be readily controlled for output modes which can be up to one octave apart. The two downconverted modes, which exhibit the greater violations of the steering inequalities, can also be controlled to exhibit asymmetric steering in some regimes.

quant-ph↗
arXiv2017

Quantum difference parametric amplification and oscillation

A recent article [W.C.W. Huang and H. Batelaan, arXiv:1708.0057v1] analysed the dualism between optical and difference parametric amplification, performing a classical analysis of a system where two electromagnetic fields are produced by another of a frequency which is the difference of the frequency of the other two. The authors claimed that this process would not violate energy conservation at the classical level, but that a quantum description would necessarily require a non-Hermitian Hamiltonian and therefore would not exist. In this work we show that the process can proceed quantum mechanically if described by the correct Hamiltonian, that energy conservation is not violated, and that fields are produced with interesting quantum statistics. Furthermore, we show that the process can be thought of as different types of already known three-wave mixing processes, with the actual type depending on either initial conditions or personal preference.

quant-ph↗
arXiv2017

Tripartite correlations over two octaves from cascaded harmonic generation

We analyse the output quantum tripartite correlations from an intracavity nonlinear optical system which uses cascaded nonlinearities to produce both second and fourth harmonic outputs from an input field at the fundamental frequency. Using fully quantum equations of motion, we investigate two parameter regimes and show that the system produces tripartite inseparability, entanglement and EPR steering, with the detection of these depending on the correlations being considered.

quant-ph↗
arXiv2017

Finite-time Lyapunov exponents in chaotic Bose-Hubbard chains

Many-site Bose-Hubbard lattices display complex semiclassical dynamics, with both chaotic and regular features. We have characterised chaos in the semiclassical dynamics of short Bose-Hubbard chains using both stroboscopic phase space projections and finite-time Lyapunov exponents. We found that chaos was present for intermediate collisional nonlinearity in the open trimer and quatramer systems, with soft chaos and Kolmogoroff-Arnold-Moser islands evident. We have found that the finite-time Lyapunov exponents are consistent with stroboscopic maps for the prediction of chaos in these small systems. This gives us confidence that the finite-time Lyapunov exponents will be a useful tool for the characterisation of chaos in larger systems, where meaningful phase-space projections are not possible and the dimensionality of the problem can make the standard methods intractable.

nlin.CD↗
arXiv2017

Quantum behaviour of pumped and damped triangular Bose Hubbard systems

We propose and analyse analogs of optical cavities for atoms using three-well Bose-Hubbard models with pumping and losses. We consider triangular configurations. With one well pumped and one damped, we find that both the mean-field dynamics and the quantum statistics show a quantitative dependence on the choice of damped well. The systems we analyse remain far from equilibrium, preserving good coherence between the wells in the steady-state. We find quadrature squeezing and mode entanglement for some parameter regimes and demonstrate that the trimer with pumping and damping at the same well is the stronger option for producing non-classical states. Due to recent experimental advances, it should be possible to demonstrate the effects we investigate and predict.

quant-ph↗
arXiv2017

Entanglement properties of third harmonic generation via direct and cascaded parametric processes

We compare the bipartite entanglement and EPR-steering properties of the two different schemes which produce third harmonic optical fields from an input field at the fundamental frequency. The first scheme uses second harmonic cascaded with sum-frequency generation while the second uses triply degenerate four-wave mixing, also known as direct third harmonic generation. We examine and compare the two schemes in both the travelling wave and intra-cavity configurations. We find that both schemes produce continuous-variable bipartite entanglement and EPR-steering. The direct scheme produces a greater degree of EPR-steering while the cascaded scheme allows for greater flexibility in having three available bipartitions.

quant-ph↗
arXiv2017

Quantum behaviour of open pumped and damped Bose-Hubbard trimers

We propose and analyse analogs of optical cavities for atoms using three-well inline Bose-Hubbard models with pumping and losses. With one well pumped and one damped, we find that both the mean-field dynamics and the quantum statistics show a qualitative dependence on the choice of damped well. The systems we analyse remain far from equilibrium, although most do enter a steady-state regime. We find quadrature squeezing, bipartite and tripartite inseparability and entanglement, and states exhibiting the EPR paradox, depending on the parameter regimes. We also discover situations where the mean-field solutions of our models are noticeably different from the quantum solutions for the mean fields. Due to recent experimental advances, it should be possible to demonstrate the effects we predict and investigate in this article.

quant-ph↗
arXiv2017

A quantum correlated twin atom laser from a Bose-Hubbard system

We propose and evaluate a method to construct a quantum correlated twin atom laser using a pumped and damped Bose-Hubbard inline trimer which can operate in a stationary regime. With pumping via a source condensate filling the middle well and damping using either an electron beam or optical means at the two end wells, we show that bipartite quantum correlations build up between the ends of the chain, and that these can be measured either in situ or in the outcoupled beams. While nothing similar to our system has yet been achieved experimentally, recent advances mean that it should be practically realisable in the near future.

quant-ph↗
arXiv2016

Pseudo steady-state non-Gaussian EPR-steering of massive particles in pumped and damped Bose-Hubbard dimers

We propose and analyse a pumped Bose-Hubbard dimer as a source of continuous-variable Einstein-Podolsky-Rosen (EPR) steering with non-Gaussian statistics. We use the truncated Wigner representation to calculate third and fourth order cumulants, finding clear signals of non-Gaussianity. We also calculate the products of inferred quadrature variances which indicate that states demonstrating the EPR paradox are present. Our proposed experimental configuration is extrapolated from current experimental techniques and adds another possibility to the current toolbox of quantum atom optics.

quant-ph↗
arXiv2016

Finite size effects and equilibration in Bose-Hubbard chains with central well dephasing

We investigate Bose-Hubbard chains in a central depleted well configuration, with dephasing in the middle well. We look at equilibration of populations, pseudo-entropy, and entanglement measures. Using stochastic integration in the truncated Wigner representation, we find that the initial quantum states of the occupied wells has an influence on the subsequent dynamics, and that with more than three wells, the chains do not reach a full equilibrium, with edge effects becoming important, and the time to reach the steady state becoming longer. The evolutions with and without phase diffusion are qualitatively different. We find no convincing evidence of entanglement in the final states with phase diffusion. Although at least one accepted measure indicates the presence of mode entanglement, we are easily able to show that it can give ambiguous predictions.

quant-ph↗
arXiv2016

Correspondence between stochastic Wigner trajectories and individual experimental runs

We examine the interpretation of individual phase-space trajectories of the Wigner function as corresponding to possible outcomes of single experimental trials. To this end, we investigate the relation between the true (measured) particle number distribution $P_n$ for a single-mode state and that obtained by discretely binning the individual stochastic realisations of squared mode amplitudes $|α|^2$ of the sampled Wigner distribution $W(α)$, which we denote via $\tilde{P}_n$. We provide an operational definition of $\tilde{P}_n$ in terms of the underlying Wigner function, which allows us to explicitly calculate the overlap between the two number distributions and hence quantify the statistical distance between them. We find that there is indeed a close quantitative correspondence between $P_n$ and $\tilde{P}_n$ for a wide range of states, justifying the broadly accepted view that, for highly occupied modes, individual stochastic realisations of Wigner trajectories should approximately correspond to outcomes of single experiments. However, we also find counterexamples for which high mode occupation may not be sufficient for such an interpretation, we find instead that a more relevant and sufficient requirement is the smoothness and broadness of the Wigner function $W(α)$ for the state of interest relative to the scale of oscillations of the Wigner functions for the relevant Fock states.

quant-ph↗
arXiv2016

Approximate particle number distribution from direct stochastic sampling of the Wigner function

We consider the Wigner quasi-probability distribution function of a single mode of an electromagnetic or matter-wave field to address the question of whether a direct stochastic sampling and binning of the absolute square of the complex field amplitude can yield a distribution function $\tilde{P}_n$ that closely approximates the true particle number probability distribution $P_n$ of the underlying quantum state. By providing an operational definition of the binned distribution $\tilde{P}_n$ in terms of the Wigner function, we explicitly calculate the overlap between $\tilde{P}_n$ and ${P}_n$ and hence quantify the statistical distance between the two distributions. We find that there is indeed a close quantitative correspondence between $\tilde{P}_n$ and $P_n$ for a wide range of quantum states that have smooth and broad Wigner function relative to the scale of oscillations of the Wigner function for the relevant Fock state. However, we also find counterexamples, including states with high mode occupation, for which $\tilde{P}_n$ does not closely approximate $P_n$.

quant-ph↗
arXiv2016

The versatility of continuous-variable asymmetric tripartite entanglement allows Alice and Clare to keep secrets from Bob

The fully symmetric Gaussian tripartite entangled pure states will not exhibit two-mode Einstein Podolsky-Rosen (EPR)-steering. This means that any two participants cannot share quantum secrets using the security of one-sided device independent quantum key distribution (1SDI-QKD) without involving the third. They are restricted at most to standard quantum key distribution (S-QKD), which is less secure. Here we show that least some asymmetric tripartite systems can exhibit bipartite EPR-steering, so that two of the participants can use 1SDI-QKD without involving the other. This is possible because the promiscuity relations of continuous-variable tripartite entanglement are different from those of discrete-variable systems. We analyse these properties for two different systems, showing that the asymmetric system has an extra degree of flexibility not found in the symmetric one.

quant-ph↗