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arXiv:1306.2525 · Physical Review A

Optimal squeezing in the resonance fluorescence of single-photon emitters

P. Grünwald, W. Vogel

Published Aug 21, 2013• 17 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.88.023837

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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.
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.
We consider a two-level atom in an optical cavity driven by a coherent field and coupled to broadband squeezed vacuum. In the bad-cavity limit, the cavity field can be adiabatically eliminated, leaving equations of motion for atomic operators similar to those of free-space resonance fluorescence. We calculate the incoherent spectrum of the fluorescent light field and find that the cavity-enhanced spontaneous emission can be suppressed, and a subnatural linewidth obtained, for the correct choice of the phase of the squeezed input relative to the coherent driving field.
Resonance fluorescence of natural or artificial atoms constitutes a prime method for generating non-classical light. While most efforts have focused on producing single photons, multi-photon emission is unavoidably present in the resonant driving of an atom. Here, we study the extent to which these processes occur: we quantify the multi-photon emission statistics in a resonantly driven two-level artificial atom—a semiconductor quantum dot in a micropillar cavity—when pumped by short optical pulses. By measuring auto-correlation functions up to the fourth order, we observe up to four photons emitted after a single pumping pulse and investigate the emission dynamics with finely resolved temporal measurements. Furthermore, we propose a method based on acquisition time gating to enhance the purity of a single-photon source while maintaining high efficiencies. Our results deepen the understanding of the photon emission processes in coherently driven atomic systems and suggest a simple but effective technique to reduce the multi-photon components of a single-photon source.
We theoretically demonstrate the enhanced and dephasing-immune squeezing in the resonance fluorescence of a single quantum dot (QD) confined to a pillar microcavity and driven by a continuous wave laser. We employ a formalism based on polaron master equation theory for incorporating the influence of exciton-phonon coupling quite accurately in the dot-cavity system. We show a significant enhancement of squeezing due to cavity coupling of the QD as compared to that of an ideal single two-level system in free space. Particularly, we show a fourfold enhancement in squeezing as compared to that of a single QD without cavity coupling. We further demonstrate the persistence of squeezing even when the pure dephasing becomes greater than the radiative decay rate. These features are attributed to the cavity-enhanced coherence causing partial reduction of the deteriorating effects of phonon-induced incoherent rates. We also show that the deteriorating effects of phonon-induced incoherent rates on squeezing can be partially circumvented by properly adjusting the detunings.
Light emitted from laser-driven atoms often has squeezed quadrature fluctuations reflecting the phase dependence of the atomic source excited into a coherent superposition by the driving field. In this paper, we study the maximum squeezing in the emitted light fields from three-level atoms, paying particular attention to the role of atomic coherences in governing the optimum squeezing which is possible. Some phase dependent nonlinear optical processes have the potential for substantial quantum noise reduction at useful intensities: for example, four-wave mixing involving atomic systems has already been used to generate quadrature-squeezed light. The threoretical description of such a source is generally complicated with damping processes, coherent and incoherent pumping, and so on, all needing to be taken into account. Fully quantum treatments are available, but the basic physics of the process is often difficult to grasp in the necessarily complicated analysis. Although less important from the point of view of efficient practical sources of squeezed light, studying the generation of squeezed light in simpler systems such as two- or three-level atoms interacting with one or two modes (as in Jaynes-Cummings models) or in spontaneous emission or resonance fluorescence gives greater insight into the fundamentals of the squeezing process. In particular, the relationship between the atomic coherences and the degree of squeezing in the generated fields can be explored. We study the maximum (optimized) squeezing that can be obtained in the emitted fields from the irreversible decay from three-level atoms for any choice of initial conditions, excitations and decay process, for all quadrature components and for all possible configurations (V, \ensuremath{\Lambda}, and ``ladder'' systems).We show that for V and \ensuremath{\Lambda} systems, optimum squeezing is actually associated with a two-level state (in a suitable basis) involving a single one-photon coherence, but for ladder systems the state for maximum noise reduction is not equivalent to a two-level system and involves a single two-photon coherence and no intermediate state population. We pay particular attention to whether the total field is in a minimum uncertainty state, and the nature of the atomic state associated with maximum squeezing, especially whether it is a mixed or pure state. In the case where the initial free field has a zero amplitude at the detector and the source atoms are confined to a region small compared to the wavelength (Dicke source) we show that the squeezing in the total field is given in terms of the squeezing in the source field, and hence related to atomic populations and atomic one-photon and two-photon coherences for the case of three level atom. Previously unconsidered source-free field interferences terms are shown to be zero. The choice of quadrature phase and frequency is optimized to minimize the source field normally ordered variance. We then minimize further with respect to the choice of atomic density matrix elements subject to the constraints that the density matrix is Hermitean, positive, and has a trace equal to unity. In all cases we find that the optimum squeezing is produced when the source field is in a minimum uncertainty state.
We propose a conditional generation of quantum squeezing from realistic single-photon states. The proposed method does not require any coherent measurement projecting on a superposition of internal levels inside single-photon emitters. Interestingly, the squeezing can be generated despite a low single-photon efficiency of the emitters. The method can therefore substantially enlarge the set of existing sources of the squeezed states of electromagnetic radiation. For example, it can be used to produce squeezed ultraviolet radiation based on already available ultraviolet single-photon emitters.