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Physical Review A

Four-level atomic interferometer driven by shaped ultrafast laser pulses

Stephen D. Clow, Thomas C. Weinacht

Published Aug 12, 2010• 9 citations
Publisher

Abstract

We analyze the behavior of a four-state, two-path atomic interferometer driven by shaped ultrafast laser pulses. The laser pulses interact with atomic rubidium, exciting the atoms to the $5D$ state via two intermediate resonances (the $5{P}_{1/2}$ and $5{P}_{3/2}$). The relative phase of the two paths can be modified by applying a varying spectral phase at the wavelength corresponding to one of the resonant transitions for each pathway. We trace out the behavior of the system from the simplest case of weak-field excitation with resonant fields to strong-field excitation with a broadband source. Our measurements and analysis reveal that while interference is observed for all field strengths and spectral widths, the character of the interference changes substantially.

DOI
10.1103/physreva.82.023411

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We analyze the behavior of a four-state, two-path atomic interferometer driven by shaped ultrafast laser pulses. The laser pulses interact with atomic rubidium, exciting the atoms to the 5D5D5D state via two intermediate resonances (the 5P1/25{P}_{1/2}5P1/2​ and 5P3/25{P}_{3/2}5P3/2​). The relative phase of the two paths can be modified by applying a varying spectral phase at the wavelength corresponding to one of the resonant transitions for each pathway. We trace out the behavior of the system from the simplest case of weak-field excitation with resonant fields to strong-field excitation with a broadband source. Our measurements and analysis reveal that while interference is observed for all field strengths and spectral widths, the character of the interference changes substantially.
We investigate coherent control of the two-photon transition pathways of a four-level atomic system in a diamond configuration. When an ultrashort laser pulse interacts with this system in the ground state 5S1/25{S}_{1/2}5S1/2​ of rubidium, the two-photon transition probability amplitude of 5D3/25{D}_{3/2}5D3/2​ is obtained by a summation of all possible resonant and nonresonant two-photon transition probability amplitudes via 5P1/25{P}_{1/2}5P1/2​ and 5P3/25{P}_{3/2}5P3/2​. Second-order perturbation theory predicts that the maximal constructive interference of the transition probability amplitudes occurs when the phases of eight different spectrum blocks satisfy four different phase relations. Experiments carried out with spectrally phase-coded laser pulses show good agreement with the theoretical prediction.
There is an increasing interest in the extraction and control of the interfering quantum pathway amplitudes induced by control fields during laser-matter interactions. The Hamiltonian-encoding and observable-decoding (HE-OD) technique has been introduced for extracting the amplitudes of the pathways present in the dynamics and has recently been experimentally applied to the pathway manipulation of atomic rubidium. This paper theoretically explores various strategies for manipulating pathway amplitudes in the context of a laser field interacting with a multilevel system similar to atomic rubidium for both narrow-band and broadband ultrafast fields. In the perturbation regime, two second-order quantum pathways connecting the Rb states 5S1/25{S}_{1/2}5S1/2​ and 5D3/25{D}_{3/2}5D3/2​ dominate the dynamics, namely, $5{S}_{1/2}\ensuremath{\rightarrow}5{P}_{3/2}\ensuremath{\rightarrow}5{D}_{3/2}$ (pathway 1) and $5{S}_{1/2}\ensuremath{\rightarrow}5{P}_{1/2}\ensuremath{\rightarrow}5{D}_{3/2}$ (pathway 2). For narrow-band field control, the analysis is carried out in the time domain with the laser field including only four narrow-band envelope subpulses centered at the resonant frequencies. When the two pathways cooperate constructively, temporal oscillations appear in the ratio of the two pathway amplitudes, and we conclude in this case that the period corresponds to the detuning between transitions $5{S}_{1/2}\ensuremath{\rightarrow}5{P}_{3/2}$ and $5{P}_{3/2}\ensuremath{\rightarrow}5{D}_{3/2}$. For broadband field control, the dynamics are treated in the frequency domain with the laser field including both resonant and continuous nonresonant frequency components. Various control strategies based on manipulating the phase of selected spectral components are tested. Compared to the outcome from a transform limited pulse, a $\frac{\ensuremath{\pi}}{2}$ step scheme can increase the dynamic range of the ratio between the two pathway amplitudes by a factor of $\ensuremath{\sim}3$. A scheme that manipulates eight spectral blocks, in which the spectral boundaries depend on the resonant frequencies, can increase the ratio by several orders of magnitude. Numerical simulations show that further dividing the spectrum into hundreds of evenly spaced blocks does not significantly enhance the pathway ratio over the eight-block scheme. The quantum control of pathways investigated in this work provides valuable insights on how to incorporate known information about the structure of quantum systems for the effective reduction of quantum control complexity.
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.
In this thesis, atomic coherence is used to enhance nonlinear optical processes in multi-level atoms. The multi-photon transitions are driven resonantly, and at the same time without absorptive losses, by using electromagnetically induced transparency (EIT), thereby allowing the study of χ(3) and χ(5) nonlinearities using weak driving fields. The coherently modified probe beam(s) and the atom-radiated signal fields arising from four- and six- wave- mixing (FWM and SWM) processes are measured in the spectral, temporal and spatial domains. In a three-level ladder-type atomic system, multiple peaks having spectral asymmetries are observed in the EIT window as well as in the FWM signal waveforms due to the diverse multiplicities of the participating atomic states. Using phase control tailored in the frequency domain, we demonstrate all-optical methods to control these spectral waveforms and discuss applications involving waveform-shaping and metrology. For the EIT study we demonstrate a switching of multiple dark peaks into bright peaks via phase-control of interferences in the underlying dark-states. In the FWM study we demonstrate all-optical spectral line shape symmetrization, linewidth narrowing and bandwidth switching. In a four-level inverted-Y-type atomic system, we drive and measure coexisting and phase-matched FWM and SWM signals. By using precision control of the relative phase and amplitude between these two processes of different nonlinear orders, we demonstrate phase coherence between them. First, a single-phase measurement is performed in the temporal and spatial domains, and the interferogram is used to measure the resonant frequency of the 5D5/2-5P3/2 atomic transition in 85Rb. Second, the method is extended to realize a capacity for two-phase measurement. In this case, the spectral bandwidth of the signal is modified in order to measure the phase-shift occurring in one Mach-Zehnder interferometer, while the intensity of the total signal waveform measures the phase-shift occurring in a second interferometer. Finally, we demonstrate phase-dependent spatial fusion between two ultra-weak optical fields by using a strong coupling field to first convert the weak fields into bosonic dark-state polaritons, which are then steered into a common all-optical waveguide mode arising due to the coupling field's intensity distribution and the resulting cross-Kerr refractive index gradient.
In this thesis, we present work on coherent control of multilevelquantum systems in the strong field limit using shaped ultrafastlaser pulses. In recent years there have been numerous multiphotonabsorption experiments in two,three, and four-level atomic/molecularsystems and many are performed in the limit of weak fields whereperturbation theory is valid. Here, we describe a series ofexperiments aimed at exploring and understanding multiphotontransitions when the exciting field is strong and perturbationtheory breaks down. Our approach to strong field control utilizesboth parameterized scans of various pulse shapes and closed-looplearning control to identify a pulse shape that is optimal forpopulating a target quantum state. With this we will highlight thedifference between sequential population transfer and adiabaticrapid passage in multilevel systems with multiphoton couplingbetween levels. Additionally, we examine strong field control of afour-level atomic interferometer and show how interference in atarget state changes from resonant pathways in the frequency domainto time-domain interference via a singe path.Further, we use shaped femtosecond pulses to demonstrate aphenomenon in which a three-level atom becomes a modulator of anultrafast pulse. The results are based on a pump-probe scheme thatis very similar to Electromagnetically Induced Transparency (EIT).Important dynamics associated with a time-dependent coupling fieldare examined. Lastly, we extend previous work on two-photon drivensuperfluorescence from a shaped ultrafast drive laser and show howstimulated emission near threshold can turn modest coherent controlyields into essentially perfect discrimination between systems wherea control factor of about 104 is achieved between atomic andmolecular species.
We demonstrate temporal coherent control in two-photon transitions. A pair of broadband (Δλ∼20nm), ultrashort (Δt∼100fs), collinear pulses with a variable time delay excites the rubidium atoms into the 5D state from the 5S ground state where the two-photon transitions are enhanced by the intermediate level 5P. The excited atoms radiate 5μm (5D–6P) and 420nm (6P–5S) light. As a result of tuning the wavelength of the input laser, a superfluorescence at 420nm exhibits different temporal behaviors. A switching from a beating at the frequency given by the difference between the sequential atomic transitions that involve the 5P3/2 intermediate level, to a quantum beating due to two different two-photon excitation paths, 5S→5P1/2→5D and 5S→5P3/2→5D is observed. Based on the simple atom-field interaction theory, an analytic solution, which qualitatively elucidates experimental results, is obtained.