The excitation amplitude after multiple crossings is not a mere product of Landau-Zener transition probabilities at each crossing, due to coherent evolution of the system in between crossings. In the three-level ladder system, the trapping of population by frequency modulated fields ensures coherent evolution, and inclusion of phase effects for population redistribution after multiple crossings becomes necessary. The relative phase accumulated by various adiabatic states as they evolve along different paths is tailored to show the existence of quantum interference effects. We present a method of inverting the population in a three-level system, without affecting the population in the intermediate state. We also present an all optical implementation of the three-level ladder system, where these effects can be realized.
The excitation amplitude after multiple crossings is not a mere product of Landau-Zener transition probabilities at each crossing, due to coherent evolution of the system in between crossings. In the three-level ladder system, the trapping of population by frequency modulated fields ensures coherent evolution, and inclusion of phase effects for population redistribution after multiple crossings becomes necessary. The relative phase accumulated by various adiabatic states as they evolve along different paths is tailored to show the existence of quantum interference effects. We present a method of inverting the population in a three-level system, without affecting the population in the intermediate state. We also present an all optical implementation of the three-level ladder system, where these effects can be realized.
We calculate the propagator and the transition probabilities for a coherently driven three-state quantum system. The energies of the three states change linearly in time, whereas the interactions between them are pulse shaped. We derive a highly accurate analytic approximation by assuming independent pairwise Landau-Zener transitions occurring instantly at the relevant avoided crossings, and adiabatic evolution elsewhere. Quantum interferences are identified, which occur due to different possible evolution paths in Hilbert space between an initial and a final state. A detailed comparison with numerical results for Gaussian-shaped pulses demonstrates a remarkable accuracy of the analytic approximation. We use the analytic results to derive estimates for the half-width of the excitation profile, and for the parameters required for creation of a maximally coherent superposition of the three states. These results are of potential interest in ladder climbing in alkali-metal atoms by chirped laser pulses, in quantum rotors, in transitions between Zeeman sublevels of a J=1 level in a magnetic field, and in control of entanglement of a pair of spin-1∕2 particles. The results for the three-state system can be generalized, without essential difficulties, to higher dimensions.
This paper presents observations and an interpretation of laser-induced excitation and fluorescence in a ladder $g\text{\ensuremath{-}}e\text{\ensuremath{-}}f$ of three molecular levels [$X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}({v}^{\ensuremath{''}}=0,{J}^{\ensuremath{''}}=7)$, $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}({v}^{\ensuremath{'}}=10,{J}^{\ensuremath{'}}=8)$, and $5\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}(v=10,J=9)$, respectively] observed in a supersonic molecular beam of Na2. The $g\text{\ensuremath{-}}e$ coupling, by cw laser P, is strong. A weak cw laser S couples levels e and f. The basic observations are of level-f fluorescence as a function of the detuning of the S laser from resonance. The signal profile does not appear as the typical Autler-Townes doublet, but as a spectral structure, whose position, width, and shape depend upon several laser parameters. We interpret these results using a simple model of three nondegenerate quantum states coherently excited while undergoing population loss to states outside the three-level system. We invoke the mechanism of optical pumping and evolution along adiabatic states, together with Landau-Zener transition probabilities. We also present results from numerical studies, which include all quantum states, all radiative couplings, coherent and incoherent, as well as convolutions with the relevant distribution functions (velocities and Zeeman sublevels). Although no adjustable parameters are involved, excellent agreement with the experiment is found. Since successive avoided crossings of adiabatic eigenvalues occur, interference effects may be relevant. Such effects are not expected to be visible in the present experiment, for reasons that are discussed. However, we discuss conditions which would allow resolving the interference structure experimentally. We also suggest possible interesting applications of the interference to rapidly switch off Rydberg state population or to control its spatial distribution.
Landau-Zener-St\uckelberg (LZS) interference is a common tool to study various quantum systems. When system is driven forth and back through anticrossings, phases are accumulated coherently, and results in constructive or destructive interference. LZS are widely demonstrated in two-level systems and multilevel systems. Nonetheless, multilevel physics in LZS interference of a multilevel system remains unexplored, since in most of the cases, influence of each anticrossing can be treated separately, thus two-level model is sufficient. Here, we investigate the LZS interference of multilevel systems in quantum dots (QDs), and propose a scheme to realize an effective model from the complicated energy levels. By employing this model, we study the physics in multilevel system such as Autler-Townes splitting (ATS), electromagnetically induced transparency and coherent population trapping (CPT) etc., and reveal their unique behaviors in our scheme. Specifically, possible improvement for present two-qubit gate in QDs and noise-robust quantum gates are proposed. The theoretical consideration we present is rather general, and thus is in principle valid for other quantum systems with the similar energy structure.
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.
The time evolution groups of parallel energy levels (m, m{prime} = 0, 1, 2,...) is considered as a model of dynamic state mixing of interacting Rydberg manifolds by ramped electric fields used in selective field ionization (SFI). Each intersection [m, m{prime}] of the triangular grid of level crossings is treated as an isolated 2-level Landau-Zener anticrossing with amplitudes d and a for diabatic and adiabatic transitions, respectively ({vert_bar}d{vert_bar}{sup 2} + {vert_bar}a{vert_bar}{sup 2} = 1). Beginning on the uppermost upward-going level (m = 0) and following successive time steps {tau}{sup (N)} (N = 0,1,2,...), a path analysis leads to complex interference patterns among the many paths arriving at an intersection [m, m{prime}] after passing through N = m + m{prime} previous ones. The relative phase between any two paths is a multiple of the unit of action {var_phi} defined by the two pairs of adiabatic levels connecting four neighboring anticrossings. Compared to results from an analysis neglecting interference effects, there occurs here a general {open_quotes}emptying out{close_quotes} of population at the center of the interaction region (where the majority of paths lead). Most striking are resonances at high ramp rates (d {yields} 1), which with high probability enhance upward-going levels whose indexmore » m is an integral multiple of 27{pi}/{var_phi}. Though {var_phi} is sensitive to ramp rate, it is nevertheless expected that observed diabatic SFI signals should exhibit sequences of secondary peaks traceable to such resonances, which should not be assigned to extraneous initial states.« less
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.