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arXiv:1206.6255 · Physical Review Letters

Optimal Squeezing in Resonance Fluorescence via Atomic-State Purification

P. Grünwald, W. Vogel

Published Jul 3, 2012• 21 citations
arXivHTMLPDF

Abstract

Squeezing of atomic resonance fluorescence is shown to be optimized by a properly designed environment, which can be realized by a quasiresonant cavity. Optimal squeezing is achieved if the atomic coherence is maximized, corresponding to a pure atomic quantum state. The atomic-state purification is achieved by the backaction of the cavity field on the atom, which increases the atomic coherence and decreases the atomic excitation. For realistic cavities, the coupling of the atom to the cavity field yields a purity of the atomic state of more than 99%. The fragility of squeezing against dephasing is substantially reduced in this scenario, which may be important for various applications.

DOI
10.1103/physrevlett.109.013601

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Squeezing of atomic resonance fluorescence is shown to be optimized by a properly designed environment, which can be realized by a quasiresonant cavity. Optimal squeezing is achieved if the atomic coherence is maximized, corresponding to a pure atomic quantum state. The atomic-state purification is achieved by the backaction of the cavity field on the atom, which increases the atomic coherence and decreases the atomic excitation. For realistic cavities, the coupling of the atom to the cavity field yields a purity of the atomic state of more than 99%. The fragility of squeezing against dephasing is substantially reduced in this scenario, which may be important for various applications.
The possibilities and perspectives of squeezed-light emission are studied for coherently driven single-photon sources, such as atoms and quantum dots. Maximal squeezing is realized, if the electronic subsystem of the emitter is in a pure quantum state. The purification is achieved by using a cavity as a second decay channel, aside from the incoherent coupling to the electromagnetic vacuum. For realistic cavities, this yields a purity of the electronic state of more than 99%. Aside from numerical calculations, we also derive approximate analytical results. Based on the approximations, effects are studied which originate from the environment of the emitter, including radiationless dephasing and incoherent pumping of the emitter and the cavity mode. The fragility of squeezing against decoherence is substantially reduced, so that squeezing persists even under hostile conditions. The measurement of squeezing from such light sources is also considered.
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It is shown that 100100%100 squeezed output can be produced in the resonance fluorescence from a coherently driven two-level atom interacting with a squeezed vacuum. This is only possible for N=1/8N=1/8N=1/8 squeezed input, and is associated with a pure atomic state, i.e., a completely polarized state. The quadrature for which optimal squeezing occurs depends on the squeezing phase $\ensuremath{\Phi}$, the Rabi frequency $\ensuremath{\Omega}$, and the atomic detuning $\ensuremath{\Delta}$. Pure states are described for arbitrary $\ensuremath{\Phi}$, not just $\ensuremath{\Phi}=0$ or $\ensuremath{\pi}$ as in previous work. For small values of N, there may be a greater degree of squeezing in the output field than the input, i.e., we have squeezing amplification.
We investigate the modification of squeezing spectrum of resonance fluorescence of a weakly driven two-level atom coupled with a frequency-tunable cavity mode with finite bandwidth. For atom-laser resonance or small atom-laser detuning, as the cavity resonant frequency adjusted, the squeezing switches between the phase quadratures. When the coupling between the atom and the cavity increases, the degree of squeezing in the out-of-phase quadrature decreases, while the noise in the in-phase quadrature decreases and can be squeezed. For proper atom-laser detuning, with the cavity-laser detuning increasing, the degree of squeezing in the in-phase quadrature increases and the squeezing spectrum exhibits two-mode squeezing.
The squeezing properties of the fluorescence field emitted by a two-level atom driven by a coherent laser field in a squeezed vacuum are calculated. We show that in the region of the anomalous resonance fluorescence the emitted field exhibits squeezing that is much larger than that in the input squeezed vacuum. The squeezing spectrum attains a minimum value that corresponds to 75% squeezing. We also find that, in the total fluorescence field, squeezing attains an optimum achievable value in the fluorescence field emitted by a two-level atom. The optimum squeezing is associated with the collapse of the system into a pure state.