Non-classical properties and quantum interference (QI) in two-photon excitation of
a three level atom (|1〉), |2〉, |3〉) in a ladder configuration, illuminated by multiple
fields in non-classical (squeezed) and/or classical (coherent) states, is studied. Fundamentally
new effects associated with quantum correlations in the squeezed fields
and QI due to multiple excitation pathways have been observed. Theoretical studies
and extrapolations of these findings have revealed possible applications which are
far beyond any current capabilities, including ultrafast nonlinear mixing, ultrafast
homodyne detection and frequency metrology. The atom used throughout the experiments
was Cesium, which was magneto-optically trapped in a vapor cell to produce
a Doppler-free sample. For the first part of the work the |1〉 → |2〉 → |3〉 transition
(corresponding to the 6S1/2F = 4 → 6P3/2F' = 5 → 6D5/2F = 6 transition) was
excited by using the quantum-correlated signal (Ɛs) and idler (Ɛi) output fields of a
subthreshold non-degenerate optical parametric oscillator, which was tuned so that
the signal and idler fields were resonant with the |1〉 → |2〉 and |2〉 → |3〉 transitions,
respectively. In contrast to excitation with classical fields for which the excitation
rate as a function of intensity has always an exponent greater than or equal to two,
excitation with squeezed-fields has been theoretically predicted to have an exponent
that approaches unity for small enough intensities. This was verified experimentally
by probing the exponent down to a slope of 1.3, demonstrating for the first time a
purely non-classical effect associated with the interaction of squeezed fields and atoms.
In the second part excitation of the two-photon transition by three phase coherent
fields Ɛ1 , Ɛ2 and Ɛ0, resonant with the dipole |1〉 → |2〉 and |2〉 → |3〉 and quadrupole
|1〉 → |3〉 transitions, respectively, is studied. QI in the excited state population is
observed due to two alternative excitation pathways. This is equivalent to nonlinear
mixing of the three excitation fields by the atom. Realizing that in the experiment
the three fields are spaced in frequency over a range of 25 THz, and extending this
scheme to other energy triplets and atoms, leads to the discovery that ranges up to
100's of THz can be bridged in a single mixing step. Motivated by these results,
a master equation model has been developed for the system and its properties have
been extensively studied.
Non-classical properties and quantum interference (QI) in two-photon excitation of
a three level atom (|1〉), |2〉, |3〉) in a ladder configuration, illuminated by multiple
fields in non-classical (squeezed) and/or classical (coherent) states, is studied. Fundamentally
new effects associated with quantum correlations in the squeezed fields
and QI due to multiple excitation pathways have been observed. Theoretical studies
and extrapolations of these findings have revealed possible applications which are
far beyond any current capabilities, including ultrafast nonlinear mixing, ultrafast
homodyne detection and frequency metrology. The atom used throughout the experiments
was Cesium, which was magneto-optically trapped in a vapor cell to produce
a Doppler-free sample. For the first part of the work the |1〉 → |2〉 → |3〉 transition
(corresponding to the 6S1/2F = 4 → 6P3/2F' = 5 → 6D5/2F = 6 transition) was
excited by using the quantum-correlated signal (Ɛs) and idler (Ɛi) output fields of a
subthreshold non-degenerate optical parametric oscillator, which was tuned so that
the signal and idler fields were resonant with the |1〉 → |2〉 and |2〉 → |3〉 transitions,
respectively. In contrast to excitation with classical fields for which the excitation
rate as a function of intensity has always an exponent greater than or equal to two,
excitation with squeezed-fields has been theoretically predicted to have an exponent
that approaches unity for small enough intensities. This was verified experimentally
by probing the exponent down to a slope of 1.3, demonstrating for the first time a
purely non-classical effect associated with the interaction of squeezed fields and atoms.
In the second part excitation of the two-photon transition by three phase coherent
fields Ɛ1 , Ɛ2 and Ɛ0, resonant with the dipole |1〉 → |2〉 and |2〉 → |3〉 and quadrupole
|1〉 → |3〉 transitions, respectively, is studied. QI in the excited state population is
observed due to two alternative excitation pathways. This is equivalent to nonlinear
mixing of the three excitation fields by the atom. Realizing that in the experiment
the three fields are spaced in frequency over a range of 25 THz, and extending this
scheme to other energy triplets and atoms, leads to the discovery that ranges up to
100's of THz can be bridged in a single mixing step. Motivated by these results,
a master equation model has been developed for the system and its properties have
been extensively studied.
Two-photon excitation of a three-level atom in a ladder configuration $(\stackrel{\ensuremath{\rightarrow}}{1}\stackrel{\ensuremath{\rightarrow}}{2}3)$ by simultaneous illumination with fields in squeezed vacuum and coherent states results in quantum interference for the excitation process. The particular configuration considered here is one for which the signal and idler output fields of a subthreshold nondegenerate optical parametric oscillator are in resonance with the two-stepwise dipole atomic transitions $(\stackrel{\ensuremath{\rightarrow}}{1}2,\stackrel{\ensuremath{\rightarrow}}{2}3),$ while a ``reference oscillator'' field is in two-photon resonance with the quadrupole transition $(\stackrel{\ensuremath{\rightarrow}}{1}3).$ In an extension of the work of Ficek and Drummond [Phys. Rev. A 43, 6247 (1991)], a theoretical formulation based on the full quantum master equation for the problem is presented. The combined effects of quantum interference and the nonclassical character of the squeezed state are investigated, and offer the potential for a new detection strategy for quantum fluctuations of the electromagnetic field with ultrahigh frequencies (10's--100's THz). Based on the theory developed, we analyze quantum interference in excitation in several special cases relevant to experimental realizations, including the effects of a small focusing angle of the squeezing onto the atoms, and unusual population inversions. Special emphasis is given to identifying intrinsically quantum optical field effects versus classical field effects. Procedures that could distinguish between the two (i.e., classical and nonclassical) are suggested.
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.
This dissertation deals with theoretical and experimental research on nonclassical, or entangled, states of atoms and photons. In the first part, I describe two approaches to the preparation of entangled states of a large number of atoms. The first approach is based on the transfer of quantum correlations from non-classical light to the atomic spins. I consider three different situations: (a) the atoms are placed in a loss-free cavity and no relaxation of any kind is present; (b) the atoms are placed in a cavity with input and output for the electromagnetic field and the atoms spontaneously decay from the upper state; (c) there is no cavity around the atoms and spontaneous emission is present. I show that in all three situations with judicious choice of parameters, entangled samples of atoms can be produced. The second approach is based on quantum-nondemolition (QND) measurements of collective atomic operators. I describe experiments with pulsed and cw light as the probe, that result in squeezed spin states of atoms. When a rf magnetic field is applied to the atomic sample, sub- shot noise performance of an atomic spin interferometer is demonstrated. In the second part of the thesis I describe investigations of phase properties of two-photon and single-photon states. These experiments make use of spontaneous type-II down-conversion in a nonlinear crystal. First, interferometric measurement of a phase shift at the Heisenberg limit for a two-photon state is described. Next, a violation of Bell-type inequalities in phase space is demonstrated for the quantum optical version of the Einstein-Podolsky-Rosen state. Finally, some recent work directed toward homodyning a single photon against a strong local oscillator field is described.
Atomic coherence and interference manifested by electromagentically induced transparency (EIT) and coherent population trapping (CPT) plays an important role in the current studies of atom-photon interactions and has found numerous applications in optical physics. EIT is created in a three-level atomic system by a coupling field and results in destructive interference between two excitation paths of a weak probe laser interacting with the atomic medium. This leads to suppressed linear absorption and rapidly varying atomic dispersion for the probe laser near the atomic resonance, which provides the platform for a variety of applications such as nonlinear optics at low light levels, slow light manipulation, and quantum state engineering for photons and atoms. Here we extend the simple three-level EIT system to more complicated and versatile configurations in a multi-level atomic system coupled by multiple laser fields. We show that with multiple excitation paths provided by different laser fields, phase-dependent quantum interference is induced: either constructive or destructive interference can be realized by varying the relative phases among the laser fields. Two specific examples are discussed. One is a three-level system coupled by bichromatic coupling and probe fields, in which the phase dependent interference between the resonant two-photon Raman transitions can be initiated and controlled. Another is a four-level system coupled by two coupling fields and two probe fields, in which a double-EIT configuration is created by the phase-dependent interference between three-photon and one-photon excitation processes. We analyze the coherently coupled multi-level atomic system and discuss the control parameters for the onset of constructive or destructive quantum interference. We describe two experiments performed with cold Rb atoms that can be approximately treated as the coherently coupled three-level and four-level atomic systems respectively. The experimental results show the phase-dependent quantum coherence and interference in the multi-level Rb atomic system, and agree with the theoretical calculations based on the coherently coupled three-level or four-level model system.
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 space situational awareness scenarios, the objects needed to be characterized and identified are usually quite far away and quite dim. Thus, optical detectors need to be able to sense these very dim optical signals. Quantum interference in a three-level system can lead to amplification of optical signals. If we put a three-level system into a cavity tuned to the frequency of an incoming optical signal, we anticipate the amplification possibilities should be increased proportional to the quality factor of the cavity. Our vision is to utilize quantum dots in photonic crystal cavities, but as a stepping stone we first investigate a simple three-level system in a free-space optical cavity. We investigate quantum interference and classical interference effects when a three-level system interacts with both a cavity field mode and an external driving field mode. We find that under certain circumstances the cavity field evolves to be equal in magnitude to, but 180° out-of-phase with the external pump field when the pump field frequency equals the cavity frequency. At this point the resonance fluorescence from the atom in the cavity goes to zero due to a purely classical interference effect between the two out-of-phase fields. 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, thus allowing for a population inversion and an amplification of incoming optical signals.