Quantum Nondemolition Measurement of Large-Spin Ensembles by Dynamical Decoupling

Abstract

Quantum non-demolition (QND) measurement of collective variables by off-resonant optical probing has the ability to create entanglement and squeezing in atomic ensembles. Until now, this technique has been applied to real or effective spin one-half systems. We show theoretically that the build-up of Raman coherence prevents the naive application of this technique to larger spin atoms, but that dynamical decoupling can be used to recover the ideal QND behavior. We experimentally demonstrate dynamical decoupling by using a two-polarization probing technique. The decoupled QND measurement achieves a sensitivity 5.7(6) dB better than the spin projection noise.PACS numbers: 42.50. Lc, 07.55.Ge, 42.50.Dv, 03.67.Bg Quantum non-demolition measurement plays a central role in quantum networking and quantum metrology for its ability to simultaneously detect and generate non-classical quantum states. The original proposal by Braginsky [1] in the context of gravitational wave detection has been generalized to the optical [2, 3], atomic [4] and nano-mechanical [5] domains. In the atomic domain, QND by dispersive optical probing of spins or pseudospins has been demonstrated using ensembles of cold atoms on a clock transition [6,7], and with polarization variables [8,9], but thus far only with real or effective spin-1/2 systems.QND measurement of larger spin systems offers a metrological advantage, e.g., in magnetometry [10], and may be essential for the detection of different quantum phases of degenerate atomic gases that intrinsically rely on large-spin systems [11][12][13]. Dispersive interactions with large-spin atoms are complicated by the presence of non-QND-type terms in the effective Hamiltonian describing the interaction [14-16]. As we show, and contrary to what has often been assumed [11][12][13]17], these terms spoil the QND performance, even in the largedetuning limit. The non-QND terms introduce noise into the measured variable, or equivalently decoherence into the atomic state. The problem is serious for both large and small ensembles, so that naive application of dispersive probing fails for several of the above-cited proposals.We approach this problem using the methods of dynamical decoupling [18][19][20], which allow us to effectively cancel the non-QND terms in the Hamiltonian while retaining the QND term. To our knowledge, this is the first application of this method to quantum non-demolition measurements. Dynamical decoupling has been extensively applied in magnetic resonance [21,22], used to suppress collisional decoherence in a thermal vapor [23], to extend coherence times in solids [24], in Rydberg atoms [25], and with photon polarization [26]. Other approaches include application of a static perturbation [27,28].We consider an ensemble of spin-f atoms interacting with a pulse of near-resonant polarized light. As described in references [14][15][16], the light and atoms interact by the effective HamiltonianĤ effwhere τ is the duration of the pulse and G 1,2 are coupling constants that depend on the ato...

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

“…In special cases, the deleterious effects of the rank-2 component of the tensor polarizability can be removed via dynamical decoupling [38]. More generally, a large bias field removes the rank-2 component of the interaction that couples the collective spin to the polarization of the probe [39], leaving only internal spin dynamics that can be compensated.…”

“…(12), we find scalar (rank-0), vector (rank-1), and tensor (rank-2) contributions to the interaction. We retain only the vector contribution that leads to the Faraday effect, as the scalar contribution does not entangle photons with the atoms and the tensor contribution can in principle be removed [19]. The Faraday interaction is then,…”

“…(38). The first term describes squeezing of the variance due to measurement backaction, the second represents decay of correlations due to diffuse scattering, and the third is the noise injected into the variance from spin flips (optical pumping).…”

“…This theory accurately describes a variety of experiments including the entanglement of macroscopic ensembles in remote vapor cells [17] and quantum memory for continuous variables [2]. More recently, experiments have employed ensembles of ultracold atoms in pencil-shaped dipole traps probed by focused laser beams [18,19]. When the radiation pattern of the atomic ensemble is effectively matched with the paraxial mode of the probe, the atomic dipoles are indistinguishable and the scattering is cooperative.…”

Role of initial system-environment correlations: A master equation approach

“…It is seen that with a large N , the dynamics accounting for the nonequilibrium state of the environment due to system-state preparation is drastically different from the case without accounting for system-bath correlation. Finally, we examine what this rapid change of state implies for quantum control [43][44][45]. One of the central objectives of control is to apply control fields in order to preserve the quantum state.…”