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arXiv:quant-ph/0305167

Generating optical nonlinearity using trapped atoms

Alexei Gilchrist, Gerard J Milburn, William J. Munro, Kae Nemoto

Published May 28, 2003• 3 citations
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Abstract

We describe a scheme for producing an optical nonlinearity using an interaction with one or more ancilla two-level atomic systems. The nonlinearity, which can be implemented using high efficiency fluorescence shelving measurements, together with general linear transformations is sufficient for simulating arbitrary Hamiltonian evolution on a Fock state qudit. We give two examples of the application of this nonlinearity, one for the creation of nonlinear phase shifts on optical fields as required in single photon quantum computation schemes, and the other for the preparation of optical Schrodinger cat states.

DOI
10.48550/arxiv.quant-ph/0305167

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We describe a scheme for producing an optical nonlinearity using an interaction with one or more ancilla two-level atomic systems. The nonlinearity, which can be implemented using high efficiency fluorescence shelving measurements, together with general linear transformations is sufficient for simulating arbitrary Hamiltonian evolution on a Fock state qudit. We give two examples of the application of this nonlinearity, one for the creation of nonlinear phase shifts on optical fields as required in single photon quantum computation schemes, and the other for the preparation of optical Schrodinger cat states.
The rapidly growing field of quantum information can benefit greatly from quantum nonlinear optics, which has the potential to generate highly correlated optical states with a sufficiently large interaction strength per photon. Such states play a crucial role in various quantum applications. While the traditional approach to generating correlated optical states involves controlled interactions between individual single photons through nonlinear mediums, a more efficient approach is to use the evolution of multiphotons in the highly nonlinear optical medium. To facilitate this approach, we propose a scheme that traces the time evolution of the photons encoded in Fock space to generate complex correlated states. Our approach mimics the dynamics of many-body systems with adjustable interaction strength, allowing us to simulate state transfer on a spin chain by tuning the interaction. We also investigate the feasibility of our scheme based on current technologies and explore the potential of quantum nonlinear optics in quantum simulation.
Large bosonic or continuous variable nonlinearities can have numerous applications, ranging from the generation of cat states for quantum computation, through to quantum sensing where the sensitivity exceeds Heisenberg scaling in the resources.However, the generation of ultra-large nonlinearities has proved immensely challenging experimentally.We describe a novel protocol where one can effectively generate large Kerr-type nonlinearities via the conditional application of a linear operation on an optical mode by an ancilla mode, followed by a measurement of the ancilla and corrective operation on the probe mode.Our protocol can generate high-quality Schrödinger cat states useful for quantum computing and can be used to perform sensing of an unknown rotation or displacement in phase space, with super-Heisenberg scaling in the resources.We finally describe a potential experimental implementation using atomic ensembles interacting with optical modes via the Faraday effect.
The achievement of sufficiently fast interactions between two optical fields at the few-photon level would provide a key enabler for a broad range of quantum technologies. One critical hurdle in this endeavor is the lack of a comprehensive quantum theory of the generation of nonlinearities by ensembles of emitters. Distinct approaches applicable to different regimes have yielded important insights: i) a semiclassical approach reveals that, for many-photon coherent fields, the contributions of independent emitters add independently allowing ensembles to produce strong optical nonlinearities via EIT; ii) a quantum analysis has shown that in the few-photon regime collective coupling effects prevent ensembles from inducing these strong nonlinearities. Rather surprisingly, experimental results with around twenty photons are in line with the semi-classical predictions. Theoretical analysis has been fragmented due to the difficulty of treating nonlinear many-body quantum systems. Here we are able to solve this problem by constructing a powerful theory of the generation of optical nonlinearities by single emitters and ensembles. The key to this construction is the application of perturbation theory to perturbations generated by subsystems. This theory reveals critical properties of ensembles that have long been obscure. The most remarkable of these is the discovery that quantum effects prevent ensembles generating single-photon nonlinearities only within the rotating-wave regime; outside this regime single-photon nonlinearities scale as the number of emitters. The theory we present here also provides an efficient way to calculate nonlinearities for arbitrary multi-level driving schemes, and we expect that it will prove a powerful foundation for further advances in this area.
Quantum states of light, particularly at optical frequencies, are considered necessary to realize a host of important quantum technologies and applications, spanning Heisenberg-limited metrology, continuous-variable quantum computing, and quantum communications. Nevertheless, a wide variety of important quantum light states are currently challenging to deterministically generate at optical frequencies. In part, this is due to a relatively small number of schemes that prepare target quantum states given nonlinear interactions. Here, we present an especially simple concept for deterministically generating and stabilizing important quantum states of light, using only third-order optical nonlinearities and engineered dissipation. We show how, by considering either a nonlinear cavity with frequency-dependent outcoupling or a chain of nonlinear waveguides, one can induce high loss for all but some desired light intensities. Specifically, we find that the stabilized intensities can correspond to an evenly spaced pattern of stablilized photon numbers. This is shown to produce important quantum states with coherent superpositions between various photon numbers. As examples of this phenomenon, we show cavities which can stabilize squeezed states, as well as produce "photon-number-comb" states. Moreover, in these types of filter cavities, Glauber coherent states will deterministically evolve into Schrodinger cat states of a desired order. We discuss potential realizations in quantum nonlinear optics. More broadly, we expect that combining the techniques introduced here with additional "phase-sensitive" nonlinearities (such as second-order nonlinearity) should enable passive stabilization and generation of a wider variety of states than shown here.
Measurements play an important role in quantum computing (QC), either by providing the nonlinearity required for two-qubit gates (linear optics QC), or by implementing a quantum algorithm using single-qubit measurements on a highly entangled initial state (cluster state QC). Parity measurements can be used as building blocks for preparing arbitrary stabilizer states, and, together with one-qubit gates, are universal for quantum computing. Here we generalize parity gates by using a higher-dimensional (qudit) ancilla. This enables us to go beyond the stabilizer or graph state formalism and prepare other types of multiparticle entangled states. The generalized parity module introduced here can prepare in one shot, heralded by the outcome of the ancilla, a large class of entangled states, including Greenberger-Home-Zeilinger states GHZn{\mathrm{GHZ}}_{n}GHZn​, Wn{\mathrm{W}}_{n}Wn​, Dicke states Dn,k{\mathcal{D}}_{n,k}Dn,k​, and, more generally, certain sums of Dicke states, like Gn{G}_{n}Gn​ states used in secret sharing. For Wn{\mathrm{W}}_{n}Wn​ states it provides an exponential gain compared to linear-optics-based methods.