Atom Waves in Crystals of Light

Oberthaler, Markus K.; Abfalterer, Roland; Bernet, Stefan; Schmiedmayer, Jörg; Zeilinger, Anton

doi:10.1103/physrevlett.77.4980

Cited by 132 publications

(119 citation statements)

References 3 publications

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“…20,24,25 We will only summarize the results which are relevant for the present investigation and assume a "lambda" configuration of three atomic levels in which the laser couples levels 1 and 2 with Rabi frequency Ω, whereas level 2 decays with inverse life time γ predominantly and irreversibly to a ground (sink) state 3. 26 For a laser on resonance with the atomic transition, atoms for which no photon is detected ("undetected atoms") are governed by the following effective Hamiltonian…”

Section: Kinetic Energy Density Fluorescence and Atomic Absorp-tmentioning

confidence: 99%

Quantum kinetic energy densities: An operational approach

Muga

Seidel

Hegerfeldt

2005

The Journal of Chemical Physics

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We propose and investigate a procedure to measure, at least in principle, a positive quantum version of the local kinetic energy density. This procedure is based, under certain idealized limits, on the detection rate of photons emitted by moving atoms which are excited by a localized laser beam. The same type of experiment, but in different limits, can also provide other non positivedefinite versions of the kinetic energy density. A connection with quantum arrival time distributions is discussed.

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Section: Kinetic Energy Density Fluorescence and Atomic Absorp-tmentioning

confidence: 99%

Quantum kinetic energy densities: An operational approach

Muga

Seidel

Hegerfeldt

2005

The Journal of Chemical Physics

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“…Even in free space the correlations between position and momentum stored in an initially Airy-function-shaped wave packet can prevent spreading [2]. Here we propose and experimentally observe the formation and propagation of nondispersive atomic wave packets in an imaginary (absorptive) potential accessible in atom optics [3,4,5]. Although there is no classical force, there are correlations continuously imposed by Heisenberg's uncertainty relation resulting in the stabilization of the wave packet.…”

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confidence: 99%

Observation of Nonspreading Wave Packets in an Imaginary Potential

et al. 2005

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We propose and experimentally demonstrate a method to prepare a nonspreading atomic wave packet. Our technique relies on a spatially modulated absorption constantly chiseling away from an initially broad de Broglie wave. The resulting contraction is balanced by dispersion due to Heisenberg's uncertainty principle. This quantum evolution results in the formation of a nonspreading wave packet of Gaussian form with a spatially quadratic phase. Experimentally, we confirm these predictions by observing the evolution of the momentum distribution. Moreover, by employing interferometric techniques, we measure the predicted quadratic phase across the wave packet. Nonspreading wave packets of this kind also exist in two space dimensions and we can control their amplitude and phase using optical elements.PACS numbers: 03.75. Be, 42.50.Vk, 03.75.Dg Nonspreading wave packets have attracted interest since the early days of quantum mechanics. Already in 1926 Schrödinger [1] found that the displaced Gaussian ground state of a harmonic oscillator experiences conformal evolution because a classical force prevents the wave packet from spreading. Even in free space the correlations between position and momentum stored in an initially Airy-function-shaped wave packet can prevent spreading [2]. Here we propose and experimentally observe the formation and propagation of nondispersive atomic wave packets in an imaginary (absorptive) potential accessible in atom optics [3,4,5]. Although there is no classical force, there are correlations continuously imposed by Heisenberg's uncertainty relation resulting in the stabilization of the wave packet.Localized wave packets due to stabilization are well known in the context of periodically driven quantum systems [6] and studied with increasing interest for electronic wave packets in Rydberg atoms [7,8,9,10]. Our approach to create nondispersive atomic wave packets relies on three ingredients: (i) an absorption process [11] cuts away the unwanted parts of a broad wave creating a packet that is continuously contracting in position space, (ii) this process leads due to Heisenberg's uncertainty relation to a broadening in momentum space and consequently to a faster spreading in real space, and (iii) the absorptive narrowing and the quantum spreading are balanced, leading to a nonspreading wave packet. In the following we will refer to such a wave packet as Michelangelo packet [12].Complex potentials for matter waves [13] emerge from the interaction of near resonant light with an open twolevel system shown in Fig. 1(a). For a standing light wave tuned exactly on resonance an array of purely imaginary harmonic potentials arises. When the Rabi frequency Ω 0 is of the order of the excited state linewidth Γ the local saturation parameter |Ω 0 sin(kx)/Γ|, and thus the upper level population, is of the order of unity except in a small vicinity of the field nodes. Consequently, our system decays approximately with the rate Γ. Therefore, in the time domain t ≫ 1/Γ the atomic wave function vanishes almost...

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“…In our model all of these transitions will appear naturally through the variation of a single control parameter. There are a number of physical systems that show some of these delicate spectral properties: The EP or collapse of resonances has been observed in crystals of light [22], electronic circuits [23], propagation of light in dissipative media [24,25], vacuum Rabi splitting in semiconductors cavities [26], in microwave billiards [27,28,29,30], detuned but coupled piano strings [31], and there are a number of examples drawn from electronparamagnetic resonance [32], and solid state NMR [9]. It also may appear in many theoretical models: e.g., describing the decay of superdeformed nuclei [33], phase transitions and avoided level crossings [34,35,36], coupling of bound states to open decay channels [37], geomagnetic polarity reversal [38], tunneling between quantum dots [39,40], optical microcavity [41], vibrational surface modes [42], and in the context of the crossing of two Coulomb blockade resonances [43].…”

Section: Introductionmentioning

confidence: 99%

Dynamical regimes of a quantum SWAP gate beyond the Fermi golden rule

2008

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We discuss how the bath's memory affects the dynamics of a swap gate. We present an exactly solvable model that shows various dynamical transitions when treated beyond the Fermi Golden Rule. By moving continuously a single parameter, the unperturbed Rabi frequency, we sweep through different analytic properties of the density of states: (I) collapsed resonances that split at an exceptional point in (II) two resolved resonances ; (III) out-of-band resonances; (IV) virtual states; and (V) pure point spectrum. We associate them with distinctive dynamical regimes: overdamped, damped oscillations, environment controlled quantum diffusion, anomalous diffusion and localized dynamics respectively. The frequency of the swap gate depends differently on the unperturbed Rabi frequency. In region I there is no oscillation at all, while in the regions III and IV the oscillation frequency is particularly stable because it is determined by the environment's band width. The anomalous diffusion could be used as a signature for the presence of the elusive virtual states.

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Atom Waves in Crystals of Light

Cited by 132 publications

References 3 publications

Quantum kinetic energy densities: An operational approach

Quantum kinetic energy densities: An operational approach

Observation of Nonspreading Wave Packets in an Imaginary Potential

Dynamical regimes of a quantum SWAP gate beyond the Fermi golden rule

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