Spin Squeezing and Light Entanglement in Coherent Population Trapping

Abstract

We show that high squeezing and entanglement can be generated at the output of a cavity containing atoms interacting with two fields in a Coherent Population Trapping situation, on account of a non-linear Faraday effect experienced by the fields close to a dark-state resonance in a cavity. Moreover, the cavity provides a feedback mechanism allowing to reduce the quantum fluctuations of the ground state spin, resulting in strong steady state spin-squeezing. Close to the CPT (or dark-) resonance the fields experience a strong dispersive effect, but little absorption [3]. Consequently, several schemes have been studied which take advantage of this strong non-linearity to generate quantum correlations and squeezing in the fields under EIT or CPT conditions [7,8,9].Following the recent squeezed and entangled light states generation with cold atoms [10, 11], we study in this Letter the interaction of atoms inside an optical cavity with two field modes close to a dark-resonance. We first show that a multistable behavior for the intracavity light may occur close to the CPT resonance on account of a non-linear polarization self-rotation effect experienced by the light [12,13]. Such polarization instabilities have been observed with cold atoms [10] and thermal vapor cells [13]. We then calculate the field noise spectra and predict that strong correlations exist between the fields exiting the cavity and that squeezing and entanglement can be generated close to the switching threshold and for a wide range of parameters. In contrast with the experiments of Refs. [10,11,14] the squeezing and the entanglement are not deteriorated by excess atomic noise due to optical pumping processes and could be efficiently generated either with cold atoms or thermal vapor cells. Last, we show that under appropriate conditions on the cavity induced feedback the ground state atomic spin fluctuations may also be strongly squeezed, and subsequently read out using techniques developed within the context of quantum memory [15].We consider N Λ-like atoms with ground-states 1 and 2, interacting with two modes of the field, A 1 and A 2 . To simplify the discussion we turn to the symmetrical case of incident fields with equal power and will choose the parameters so that the Rabi frequencies of both transitions are equal: Ω i = Ω (i = 1, 2) and close to one-photon resonance. This situation corresponds to Coherent Population Trapping, since the atoms are pumped into a superposition of levels 1 and 2 -the so-called dark-statewhich is decoupled from the fields [2]. For Ω 1 = Ω 2 , this dark-state corresponds to a state with maximum ground state coherence: |D = (|1 − |2 )/ √ 2. Although this is not essential, let us note that, if levels 1 and 2 are Zeeman sublevels, the incident field can then be considered as being linearly polarized. As we will see later this facilitates the physical discussion and provides a simple picture in terms of the Stokes polarization vector and the collective spin formalism.If the fields are symmetrically detuned with respect t...

Coherence-Assisted Resonance with Sub-Transit-Limited Linewidth

“…Creating quantum correlations between two bright optical fields and also among atomic spins using CPT is currently of great interest [19,20]. Our work paves the way for the realization of such proposals, since inevitable laser frequency noise induces classical correlations in the same way as studied here [21], and understanding its behavior is necessary for achieving quantum correlations.…”

Entanglement between collective fields via phase-dependent electromagnetically induced transparency

“…A large amount of work has shown that both EIT and CPT are the bases of various coherent phenomena such as lasing with population inversion [1][2][3][7][8][9][10], enhanced frequency conversion [1][2][3][11][12][13], quantum memory for photons and nonlinear optics at low light level [4][5][6], * Corresponding author: xmhu@phy.ccnu.edu.cn. and quantum correlation, squeezing, and entanglement of light [14][15][16][17][18][19][20].…”

Polychromatic quadripartite entanglement from concurrent four-wave mixing in a three-level atomic system

“…[30][31][32][33][34][35][36]. For example, it shows that two-color highly entangled light beams can be generated via NFWM from N intracavity three-level atomic system close to electromagnetically induced transparency [37].…”