Andrew J. Ferris

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.

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.

Perfect Sampling with Unitary Tensor Networks

Tensor network states are powerful variational Ansatze for many-body ground states of quantum lattice models. The use of Monte Carlo sampling techniques in tensor network approaches significantly reduces the cost of tensor contractions, potentially leading to a substantial increase in computational efficiency. Previous proposals are based on a Markov chain Monte Carlo scheme generated by locally updating configurations and, as such, must deal with equilibration and autocorrelation times, which result in a reduction of efficiency. Here we propose perfect sampling schemes, with vanishing equilibration and autocorrelation times, for unitary tensor networks, namely, tensor networks based on efficiently contractible, unitary quantum circuits, such as unitary versions of the matrix product state (MPS) and tree tensor network (TTN), and the multiscale entanglement renormalization Ansatz (MERA). Configurations are directly sampled according to their probabilities in the wave function, without resorting to a Markov chain process. We consider both complete sampling, involving all the relevant sites of the system, and incomplete sampling, which only involves a subset of those sites and which can result in a dramatic (basis-dependent) reduction of sampling error.

Control of an atom laser using feedback

A generalized method of using feedback to control multimode behavior in Bose-Einstein condensates is introduced. We show that for any available control, there is an associated moment of the atomic density and a feedback scheme that will remove energy from the system while there are oscillations in that moment. We demonstrate these schemes by considering a condensate trapped in a harmonic potential that can be modulated in strength and position. The formalism of our feedback scheme also allows the inclusion of certain types of nonlinear controls. If the nonlinear interaction between the atoms can be controlled via a Feshbach resonance, we show that the feedback process can operate with a much higher efficiency.

Atomic entanglement generation and detection via degenerate four-wave mixing of a Bose-Einstein condensate in an optical lattice

The unequivocal detection of entanglement between two distinct matter-wave pulses is a significant challenge that has yet to be experimentally demonstrated. We describe a realistic scheme to generate and detect continuous-variable entanglement between two atomic matter-wave pulses produced via degenerate four-wave mixing from an initially trapped Bose-Einstein condensate loaded into a one-dimensional optical lattice. We perform a comprehensive numerical investigation for fixed condensate parameters to determine the maximum violation of separability and Einstein-Podolsky-Rosen inequalities for field quadrature entanglement, and describe and simulate an experimental scheme for measuring the necessary quadratures.

Dynamical instabilities of Bose-Einstein condensates at the band edge in one-dimensional optical lattices

We present a joint theoretical and experimental study of the dynamical instability of a Bose—Einstein condensate at the band edge of a one-dimensional optical lattice. The instability manifests as rapid depletion of the condensate and conversion to a thermal cloud. We consider the collisional processes that can occur in such a system, and undertake a thorough theoretical study of the dynamical instability in systems of different dimensionality. We find spontaneous scattering is an important part of this process, and thus the Gross-Pitaevskii equation is unable to accurately predict the dynamics in this system. Our beyond mean-field approach, known as the truncated Wigner method, allows us to make quantitative predictions for the processes of parametric growth and heating that are observed in the laboratory, and we find good agreement with the experimental results.

Resonator reset in circuit QED by optimal control for large open quantum systems

We study an implementation of the open GRAPE (Gradient Ascent Pulse Engineering) algorithm well suited for large open quantum systems. While typical implementations of optimal control algorithms for open quantum systems rely on explicit matrix exponential calculations, our implementation avoids these operations leading to a polynomial speed-up of the open GRAPE algorithm in cases of interest. This speed-up, as well as the reduced memory requirements of our implementation, are illustrated by comparison to a standard implementation of open GRAPE. As a practical example, we apply this open-system optimization method to active reset of a readout resonator in circuit QED. In this problem, the shape of a microwave pulse is optimized such as to empty the cavity from measurement photons as fast as possible. Using our open GRAPE implementation, we obtain pulse shapes leading to a reset time over four times faster than passive reset.

Branching MERA codes: A natural extension of classical and quantum polar codes

We introduce a new class of circuits for constructing efficiently decodable quantum and classical error-correction codes, based on a recently discovered contractible tensor network known as branching multi-scale entanglement renormalization ansatz [1]. We perform an in-depth study of a particular example that can be thought of as an extension to Arikans polar code [2]-[4]. Notably, our numerical simulation show that these codes polarize the logical channels more strongly while retaining the log-linear decoding complexity using the successive cancellation decoder. These codes also display improved error-correcting capability with only a minor impact on decoding complexity. Efficient decoding is realized using powerful graphical calculus tools developed in the field of quantum many-body physics.

Variational Monte Carlo with the multiscale entanglement renormalization ansatz

Monte Carlo sampling techniques have been proposed as a strategy to reduce the computational cost of contractions in tensor network approaches to solving many-body systems. Here, we put forward a variational Monte Carlo approach for the multiscale entanglement renormalization ansatz (MERA), which is a unitary tensor network. Two major adjustments are required compared to previous proposals with nonunitary tensor networks. First, instead of sampling over configurations of the original lattice, made of L sites, we sample over configurations of an effective lattice, which is made of just ln(L) sites. Second, the optimization of unitary tensors must account for their unitary character while being robust to statistical noise, which we accomplish with a modified steepest descent method within the set of unitary tensors. We demonstrate the performance of the variational Monte Carlo MERA approach in the relatively simple context of a finite quantum spin chain at criticality, and discuss future, more challenging applications, including two-dimensional systems.

Surpassing the standard quantum limit in an atom interferometer with four-mode entanglement produced from four-wave mixing

We theoretically investigate a scheme for atom interferometry that surpasses the standard quantum limit. A four-wave mixing scheme similar to the recent experiment performed by Pertot et al. [Phys. Rev. Lett. 104, 200402 (2010)] is used to generate subshotnoise correlations between two modes. These two modes are then interfered with the remaining two modes in such a way as to surpass the standard quantum limit, whilst utilizing all of the available atoms. Our scheme can be viewed as using two correlated interferometers. That is, the signal from each interferometer when looked at individually is classical, but there are correlations between the two interferometers that allow for the standard quantum limit to be surpassed.