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Optical and Quantum Sensing and Precision Metrology II

Photon-mediated spin-mixing dynamics

Emily J. Davis, Avikar Periwal, Eric S. Cooper, Monika Schleier-Smith, Lukas Homeier, Katherine Van Kirk, Gregory S. Bentsen

Published Mar 1, 2019• 0 citations
Publisher

Abstract

We analyze the dynamics of spin-mixing interactions generated by coupling spin-1 atoms to the mode of a high-finesse optical cavity. We show that the dynamics can be understood in terms of generators of the noncompact Lie group SU(1, 1) and introduce a set of SU(1, 1) coherent states which are preserved under Hamiltonian evolution. In terms of these coherent states the resulting dynamics may be interpreted as classical motion on the unit disk. We explicitly compute the trajectories of this classical motion and show that the motion is equivalent to spin-nematic squeezing in the atomic ensemble. Non-uniform coupling between the atomic ensemble and the cavity mode leads to departures from this simple behavior; we introduce a toy model that captures this non-uniformity and solve it exactly.

DOI
10.1117/12.2515795

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We analyze the dynamics of spin-mixing interactions generated by coupling spin-1 atoms to the mode of a high-finesse optical cavity. We show that the dynamics can be understood in terms of generators of the noncompact Lie group SU(1, 1) and introduce a set of SU(1, 1) coherent states which are preserved under Hamiltonian evolution. In terms of these coherent states the resulting dynamics may be interpreted as classical motion on the unit disk. We explicitly compute the trajectories of this classical motion and show that the motion is equivalent to spin-nematic squeezing in the atomic ensemble. Non-uniform coupling between the atomic ensemble and the cavity mode leads to departures from this simple behavior; we introduce a toy model that captures this non-uniformity and solve it exactly.
We propose a method for engineering spin dynamics in ensembles of integer-spin atoms confined within a high-finesse optical cavity. Our proposal uses cavity-assisted Raman transitions to engineer a Dicke model for integer-spin atoms, which, in a dispersive limit, reduces to effective atom-atom interactions within the ensemble. This scheme offers a promising and flexible new avenue for the exploration of a wide range of spinor many-body physics. As an example of this, we present results showing that this method can be used to generate spin-nematic squeezing in an ensemble of spin-1 atoms. With realistic parameters the scheme should enable substantial squeezing on time scales much shorter than current experiments with spin-1 Bose-Einstein condensates.
The conventional squeezed states of quantum optics, which can be thought of as generalized coherent states for the algebra SU(1,1), are dynamically generated by single-mode hamiltonians characterized by two-photon process interactions. By the explicit construction of a (highly non-linear) faithful realization of the group [Formula: see text] of automorphisms of SU(1,1), such hamiltonians are shown to be equivalent — up just to elements of [Formula: see text] — to that describing quantum mechanically a damped oscillator.
Many effects in the interaction between atoms and a cavity that are usually de-scribed in quantum mechanical terms (cavity quantum electrodynamics, cavity QED) can be understood and quantitatively analyzed within a classical framework. We adopt such a classical picture of a radiating dipole oscillator to derive explicit ex- pressions for the coupling of single atoms and atomic ensembles to Gaussian modes in free space and in an optical resonator. The cooperativity parameter of cavity QED is shown to play a central role, and is given a geometrical interpretation. The classical analysis yields transparent, intuitive results that are useful for analyzing applications of cavity QED such as atom detection and counting, cavity cooling, cavity spin squeezing, cavity spin optomechanics, or phase transitions associated with the self-organization of the ensemble-light system.
Abstract We analyze the generation of spin-squeezed states via coupling of three-level atoms to an optical cavity and continuous quantum measurement of the transmitted cavity field in order to monitor the evolution of the atomic ensemble. Using analytical treatment and microscopic simulations of the dynamics, we show that one can achieve significant spin squeezing, favorably scaling with the number of atoms N. However, contrary to some previous literature, we clarify that it is not possible to obtain Heisenberg scaling without the continuous feedback that is proposed in optimal approaches. In fact, in the adiabatic cavity removal approximation and large N limit, we find the scaling behavior N − 2 / 3 for spin squeezing and N − 1 / 3 for the corresponding protocol duration. These results can be obtained only by considering the curvature of the Bloch sphere, since linearizing the collective spin operators tangentially to its equator yields inaccurate predictions. With full simulations, we characterize how spin-squeezing generation depends on the system parameters and departs from the bad cavity regime, by gradually mixing with cavity-filling dynamics until metrological advantage is lost. Finally, we discuss the relevance of this spin-squeezing protocol to state-of-the-art optical clocks.
We propose a method for engineering spin dynamics in ensembles of integer-spin atoms confined within a high-finesse optical cavity. Our proposal uses cavity-assisted Raman transitions to engineer a Dicke model for integer-spin atoms, which, in a dispersive limit, reduces to effective atom-atom interactions within the ensemble. This scheme offers a promising and flexible new avenue for the exploration of a wide range of spinor many-body physics. As an example of this, we present results showing that this method can be used to generate spin-nematic squeezing in an ensemble of spin-1 atoms. With realistic parameters, the scheme should enable substantial squeezing on time scales much shorter than current experiments with spin-1 Bose-Einstein condensates.
The interaction between an atomic ensemble and a light mode in a high-finesse optical cavity can easily reach the strong-coupling regime, where quantum effects dominate.In this regime, the interaction can be used to generate both atom-light and atom-atom entanglement.We analyze the dominant effects on the collective atomic state and the light field, and derive a unified approach that can account for atomic entanglement induced both by measurements on the light field, and by ignoring the state of the light field altogether.We present analytical expressions for the entanglement induced by the interaction, and determine the conditions that maximize the entanglement-induced gain over the standard quantum limit in quantum sensors and atomic clocks.