R. J. Lewis-Swan

Quantum-enhanced sensing based on time reversal of nonlinear dynamics

We experimentally demonstrate a nonlinear detection scheme exploiting time-reversal dynamics that disentangles continuous variable entangled states for feasible readout. Spin-exchange dynamics of Bose-Einstein condensates is used as the nonlinear mechanism which not only generates entangled states but can also be time reversed by controlled phase imprinting. For demonstration of a quantum-enhanced measurement we construct an active atom SU(1,1) interferometer, where entangled state preparation and nonlinear readout both consist of parametric amplification. This scheme is capable of exhausting the quantum resource by detecting solely mean atom numbers. Controlled nonlinear transformations widen the spectrum of useful entangled states for applied quantum technologies.

Proposal for demonstrating the Hong–Ou–Mandel effect with matter waves

The Hong-Ou-Mandel effect is a demonstration of destructive quantum interference between pairs of indistinguishable bosons, realised so far only with massless photons. Here we propose an experiment to realize this effect in the matter-wave regime using pair-correlated atoms produced via a collision of two Bose-Einstein condensates and subjected to two laser--induced Bragg pulses. We formulate a measurement protocol for the multimode matter-wave field, which--unlike the typical two-mode optical case-bypasses the need for repeated measurements under different displacement settings of the beam splitter, markedly reducing the number of experimental runs required to map out the interference visibility. Although the protocol can be used in related matter-wave schemes, we focus on condensate collisions. By simulating the entire experiment, we predict a Hong-Ou-Mandel dip visibility of ~69%. This visibility highlights strong quantum correlations between the atoms, paving the way for a possible demonstration of a Bell inequality violation with massive particles in a related Rarity-Tapster setup.

Sensitivity to thermal noise of atomic Einstein-Podolsky-Rosen entanglement

We examine the prospect of demonstrating Einstein–Podolsky–Rosen (EPR) entanglement for massive particles using spin-changing collisions in a spinor Bose-Einstein condensate. Such a demonstration was attempted by Gross et al. [Nature 480, 219 (2011)] using a spinor condensate of Rb-87 atoms, however, the results were inconclusive. We seek to understand whether this ambiguous result could be attributed to physically important sources of noise not present in analogous quantum optics experiments, such as a small (currently undetectable) thermal seed initially present in the \(m_F = \pm 1\) substates. Specifically, our investigation focuses on how the spin-changing dynamics are altered and quantifying whether EPR entanglement can still be robustly generated.

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

We consider the Wigner quasiprobability 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 (P) over tilde (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 (P) over tilde (n) in terms of the Wigner function, we explicitly calculate the overlap between (P) over tilde (n) and Pn and hence quantify the statistical distance between the two distributions. We find that there is indeed a close quantitative correspondence between (P) over tilde (n) and Pn for a wide range of quantum states that have a 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 (P) over tilde (n) does not closely approximate P-n.

Proposal for a Motional-State Bell Inequality Test with Ultracold Atoms

In the simplest approximation, the process of spontaneous four-wave mixing via condensate collisions produces a multi-mode analog of the two-mode squeezed vacuum state. Such a state exhibits non-classical correlations, which, when combined with an appropriate measurement scheme, can be used to demonstrate a violation of a Bell inequality. In this chapter, we propose such a demonstration by realization of an atom-optics analog of a Rarity–Tapster interferometer, which was previously used in quantum optics to demonstrate a successful violation using momentum-entangled photons. Our investigation is focused on the feasibility of such a demonstration in realistic experimental regimes and responds to many of the key research questions of this thesis, such as how the violation depends on various experimental parameters and the robustness of simple ‘toy-model’ results.

Cavity-mediated collective spin-exchange interactions in a strontium superradiant laser

An atom-coupling cavity Ensembles of atoms have emerged as powerful simulators of many-body dynamics. Engineering controllable interactions between the atoms is crucial, be it direct or through a mediator. Norcia et al. developed a flexible alternative to existing atomic simulators in a system consisting of strontium atoms placed in an optical cavity. Two atomic states connected by a clock transition each served as an effective spin, with long-range spin-exchange interactions mediated by the cavity photons. With improvements, the setup is expected to be amenable to simulating nonequilibrium quantum dynamics and to have applications in metrology. Science, this issue p. 259 Engineered interactions between strontium atoms in an optical cavity lead to the emergence of a many-body energy gap. Laser-cooled and quantum degenerate atoms are being pursued as quantum simulators and form the basis of today’s most precise sensors. A key challenge toward these goals is to understand and control coherent interactions between the atoms. We observe long-range exchange interactions mediated by an optical cavity, which manifest as tunable spin-spin interactions on the pseudo spin-½ system composed of the millihertz linewidth clock transition in strontium. This leads to one-axis twisting dynamics, the emergence of a many-body energy gap, and gap protection of the optical coherence against certain sources of decoherence. Our observations will aid in the future design of versatile quantum simulators and the next generation of atomic clocks that use quantum correlations for enhanced metrology.

Solving the quantum many-body problem via correlations measured with a momentum microscope

In quantum many-body theory, all physical observables are described in terms of correlation functions between particle creation or annihilation operators. Measurement of such correlation functions can therefore be regarded as an operational solution to the quantum many-body problem. Here, we demonstrate this paradigm by measuring multiparticle momentum correlations up to third order between ultracold helium atoms in an s-wave scattering halo of colliding Bose-Einstein condensates, using a quantum many-body momentum microscope. Our measurements allow us to extract a key building block of all higher-order correlations in this system-the pairing field amplitude. In addition, we demonstrate a record violation of the classical Cauchy-Schwarz inequality for correlated atom pairs and triples. Measuring multiparticle momentum correlations could provide new insights into effects such as unconventional superconductivity and many-body localization.

Bang-bang shortcut to adiabaticity in the Dicke model as realized in a Penning trap experiment

We introduce a bang-bang shortcut to adiabaticity for the Dicke model, which we implement via a two-dimensional array of trapped ions in a Penning trap with a spin-dependent force detuned close to the center-of-mass drumhead mode. Our focus is on employing this shortcut to create highly entangled states that can be used in high-precision metrology. We highlight that the performance of the bang-bang approach is comparable to standard preparation methods, but can be applied over a much shorter time frame. We compare these theoretical ideas with experimental data which serve as a first step towards realizing this theoretical procedure for generating multi-partite entanglement.

On the Relation of the Particle Number Distribution of Stochastic Wigner Trajectories and Experimental Realizations

We consider the Wigner quasi-probability distribution function of a single mode to address the question of whether a stochastic sampling and binning of the absolute square of the complex field amplitude can yield a distribution \(\tilde{P}_{n}\) 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 \(P_{n}\) 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 \(P_{n}\).

Introduction and Background Physics

In this chapter we outline the central arguments and themes of this thesis. Specifically, we briefly discuss the well-known EPR paradox and the related Bell inequalities. The remainder of the chapter is devoted to an introduction to the key physical systems and theoretical techniques used in this thesis. In particular, we briefly cover the physical processes of spontaneous four-wave mixing and spin-changing collisions in (spinor) Bose-Einstein condensates. We also discuss the Wigner and positive P phase-space representation of quantum mechanics and give a detailed discussion of how these representations can be used to stochastically simulate large multi-mode quantum systems.