Three-dimensional light-matter interface for collective spin squeezing in atomic ensembles

Abstract

We study the three-dimensional nature of the quantum interface between an ensemble of cold, trapped atomic spins and a paraxial laser beam, coupled through a dispersive interaction. To achieve strong entanglement between the collective atomic spin and the photons, one must match the spatial mode of the collective radiation of the ensemble with the mode of the laser beam while minimizing the effects of decoherence due to optical pumping. For ensembles coupling to a probe field that varies over the extent of the cloud, the set of atoms that indistinguishably radiates into a desired mode of the field defines an inhomogeneous spin wave. Strong coupling of a spin wave to the probe mode is not characterized by a single parameter, the optical density, but by a collection of different effective atom numbers that characterize the coherence and decoherence of the system. To model the dynamics of the system, we develop a full stochastic master equation, including coherent collective scattering into paraxial modes, decoherence by local inhomogeneous diffuse scattering, and backaction due to continuous measurement of the light entangled with the spin waves. This formalism is used to study the squeezing of a spin wave via continuous quantum nondemolition (QND) measurement. We find that the greatest squeezing occurs in parameter regimes where spatial inhomogeneities are significant, far from the limit in which the interface is well approximated by a one-dimensional, homogeneous model.

Dispersive response of atoms trapped near the surface of an optical nanofiber with applications to quantum nondemolition measurement and spin squeezing

“…In free space, where there is no Purcell enhancement, strong coupling can be achieved via the cooperativity of atomic ensembles. This is most naturally implemented in a dispersive regime, off resonance, where light elastically scattered from the ensemble constructively interferes to match the mode of an exciting paraxial probe [15]. The cooperativity per atom in a typical paraxial beam is small, Γ 1D /Γ vac ∼ σ 0 /A ∼ 10 −6 .…”

Simulating Nonlinear Dynamics of Collective Spins via Quantum Measurement and Feedback

“…The proposed scheme is general and can be applied in different platforms. We consider a potential experimental implementation based on an atom-light interface [37,38] and show that our results can be robust to the effects of decoherence.…”

Enhanced cooperativity for quantum-nondemolition-measurement–induced spin squeezing of atoms coupled to a nanophotonic waveguide

“…Cooperativity also characterizes the atom-light interface in the absence of a cavity. In free space, an atom at the waist of a laser beam will scatter into the forward direction at a rate κ ∝ (σ 0 /A)γ s , where γ s is the photon scattering rate into 4π steradians [9]. Here the singleatom cooperativity can be expressed to be proportional to the ratio of these rates, C 1 ∝ κ/γ s ∝ σ 0 /A.…”

“…Here the singleatom cooperativity can be expressed to be proportional to the ratio of these rates, C 1 ∝ κ/γ s ∝ σ 0 /A. The N A -atom cooperativity, in a plane-wave approximation, * qxd@unm.edu ignoring effects of diffraction and cloud geometry [9], C N ∝ N A σ 0 /A = OD. To be self-consistent, here the beam area must be very large, so C 1 is very small, e.g., C 1 ∼ 10 −6 , but for a sufficiently large ensemble, the OD can be large enough to lead to entanglement between the collective atomic degrees of freedom and the light.…”

“…In particular, we consider the QND measurement of the collective spin of an atomic ensemble via a Faraday interaction followed by polarization spectroscopy. In this configuration the polarimeter effectively performs a homodyne measurement, where the probe is the "local oscillator," arXiv:1712.02916v3 [quant-ph] 15 Mar 2018 which interferes with the light scattered into the orthogonally polarized guided mode [9]. This signal thus depends on the spatial overlap of the two orthogonal polarization modes at the position of the atom.…”