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arXiv:quant-ph/0504147 · Journal of Modern Optics

Phase-dependent interference mechanisms in a three-level Λ system driven by a quantized laser field

Jörg Evers

Published Dec 15, 2005• 4 citations
arXivHTMLPDF

Abstract

The dynamics of an atomic few-level system can depend on the phase of driving fields coupled to the atom if certain conditions are satisfied. This is of particular interest to control interference effects, which can alter the system properties considerably. In this article, we discuss the mechanisms of such phase control and interference effects in an atomic three-level system in the Λ configuration, where the upper state spontaneously decays into the two lower states. The lower states are coupled by a driving field, which we treat as quantized. This allows for an interpretation on the single photon level for both the vacuum and the driving field. By analysing the system behaviour for a driving field initially in non-classical states with only a few Fock number states populated, we find that even though the driving field is coupled to the lower states only, it induces a multiplet of upper states. Then interference occurs independently in three-level subsystems in the V configuration, each formed by two adjacent upper states and a single dressed lower state.

DOI
10.1080/09500340500342403

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The dynamics of an atomic few-level system can depend on the phase of driving fields coupled to the atom if certain conditions are satisfied. This is of particular interest to control interference effects, which can alter the system properties considerably. In this article, we discuss the mechanisms of such phase control and interference effects in an atomic three-level system in the Λ configuration, where the upper state spontaneously decays into the two lower states. The lower states are coupled by a driving field, which we treat as quantized. This allows for an interpretation on the single photon level for both the vacuum and the driving field. By analysing the system behaviour for a driving field initially in non-classical states with only a few Fock number states populated, we find that even though the driving field is coupled to the lower states only, it induces a multiplet of upper states. Then interference occurs independently in three-level subsystems in the V configuration, each formed by two adjacent upper states and a single dressed lower state.
We consider the effect of quantum interference on population distribution and photon statistics of a cavity field interacting with dressed states of a strongly driven three-level atom. We analyse three coupling configurations of the cavity field to the driven atom, with the cavity frequency tuned to the outer Rabi sideband, the inner Rabi sideband and the central frequency of the 'singly dressed' three-level atom. The quantum doubly dressed states for each configuration are identified and the population distribution and photon statistics are interpreted in terms of transitions among these dressed states and their populations. We find that the population distribution depends strongly on quantum interference and the cavity damping. For the cavity field tuned to the outer or inner Rabi sidebands the cavity damping induces transitions between the dressed states which are forbidden for the ordinary spontaneous emission. Moreover, we find that in the case of the cavity field coupled to the inner Rabi sideband the population distribution is almost Poissonian with a large average number of photons that can be controlled by quantum interference. This system can be considered as a one-atom dressed-state laser with controlled intensity.
We discuss quantum interference effects in the resonance fluorescence spectrum of a \ensuremath{\Lambda} three-level atom when the lower-level doublet is driven by a coherent field. The interfering pathways that lead to the same final state involve both spontaneous decays and stimulated transitions, and differ from one another by an odd number of stimulated processes induced by the driving field. As a consequence, the interference structures depend upon the phase of the coherent field, an effect that is absent in other resonance fluorescence phenomena. The phase dependence of the quantum interference contribution is especially significant when the level splitting of the driven doublet is comparable to the spontaneous decay rates of the competing optical paths.
This thesis examines the effect of quantum interference occuring in a three-level atom in the V-configuration, on a variety of optical effects such as controlled spontaneous emission, population trapping, lasing without population inversion, controlled field intensity and photon statistics. Calculations are carried out numerically via the master equation approach and analytically using dressed atom analysis. Various atom-laser coupling configurations are investigated and dressed states identified in each case. The system is shown to exhibit trapping states for a variety of atom-laser coupling configurations. Moreover, the thesis focuses on the effect of quantum interference on a cavity QED system. Three different cavity detunings with respect to the entangled atom-laser system are considered. It is shown in each case how the singly dressed entangled system interacts with the cavity field to form entangled doubly dressed structures. Again, the system is shown to exhibit population trapping states with dependence on the cavity damping rate in one of the detunings considered. In addition, photon statistics of the cavity field are calculated and shown to be sensitive to the degree of quantum interference. Interestingly, controlled field intensity and sub-Poissonian statistics are obtained for certain parameters of the two off-resonance cases considered
The quantum interference in the spontaneous-emission spectrum of a driven atom, when the upper level of the atomic transition is coupled to a third level via a classical driving field, results in a dark line in the absence of the atomic decays. The existence of the dark line is independent of the Rabi frequency associated with the driving field. There is no such dark line in the spontaneous-emission spectrum when, instead of the upper level, the lower level is coupled to a third level via a driving field. In this paper, we include the level decays, incoherent pumping, and the finite bandwidth of the driving field in our analysis and study their role in the spontaneous-emission spectrum in the two configurations.
We investigate quantum interference and classical-interference effects when three-level atoms in the ``$\ensuremath{\Lambda}$'' or ``V'' configuration interact with both a cavity-field mode and an external driving field mode. We describe electromagnetically induced transparency ($\ensuremath{\Lambda}$ configuration), as well as a ``field-induced transparency'' (V configuration), and we go beyond the weak cavity-field studies of previous papers by utilizing a Heisenberg-picture density matrix approach. We find that under certain circumstances the cavity field evolves to be equal in magnitude to, but $180\ifmmode^\circ\else\textdegree\fi{}$ out of phase with, the external pump field when the pump-field frequency equals the cavity frequency, a surprising effect found in two-level atoms in a cavity excited by an external pump field that persists in three-level atoms. The better the cavity, the quicker this buildup occurs. When the cavity field reaches this ``out-of-phase'' condition, the resonance fluorescence from the atom in the cavity goes to zero. This is a purely classical-interference effect between the two out-of-phase fields, with the resonance fluorescence going to zero at the same time as the two excited state populations go to zero. This is quite different from the quantum interference that occurs under the right circumstances when the state populations are coherently driven into a linear combination that is decoupled from any applied field and population is trapped in the excited states (``coherent population trapping''). When the cavity frequency is tuned to the frequency at which quantum interference would occur, the two interference effects compete with each other. The cavity field begins to evolve toward the $180\ifmmode^\circ\else\textdegree\fi{}$ out-of-phase condition, thereby approaching a classical destructive interference condition with the pump field. Then at some point before 100% classical interference occurs, depending on the cavity damping rate and atom/cavity coupling strength, the atom builds up its coherence between state populations to produce the quantum interference effect. At that point, the atom becomes transparent and resonance fluorescence disappears, including fluorescence into the cavity, thereby causing the cavity field to die away.
In this paper we investigate the resonance fluorescence, the squeezing, and the absorption spectra of a laser-driven four-level atom consisting of three closely spaced upper levels decaying to a common lower level. The three upper levels are coupled by the same vacuum modes to the lower level leading to spontaneously generated coherence effects. High population inversion and extremely narrow emission lines are obtained with moderate Rabi frequencies, which are a direct consequence of decay-induced interferences. The fluorescent field is shown to exhibit two-mode squeezing in the in-phase quadrature. Squeezing in both quadratures simultaneously at different frequencies is greatly enhanced when quantum interference is accounted for. We also examine the absorption spectrum of a weak field and demonstrate that quantum interference can induce two prominent and nearly transparent holes where the slope of the refractive index is very steep. This special situation could allow the simultaneous propagation of two weak pulses with different frequencies, which could be feasibly exploited towards the realization of the entanglement of two photons.