Manipulating quantum wave packets via time-dependent absorption

Goussev, Arseni

doi:10.1103/physreva.91.043638

Cited by 6 publications

(15 citation statements)

References 34 publications

(39 reference statements)

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“…Time-dependent absorbing barriers may be realized in atom-optics laboratory experiments. Recently, such barriers were identified as a promising tool for engineering and reshaping (e.g., shifting, splitting, squeezing, and cooling) of atomic wave packets [21]. The main practical value of the present study is that we have extended the range of theoretical tools appropriate for investigating and making quantitative predictions related to lightbased manipulation of atomic wave functions.…”

Section: Discussionmentioning

confidence: 85%

“…As recently shown in Ref. [21], such barriers can be efficiently used to manipulate, e.g., shift, split, or squeeze, the spatial wave function of the transmitted particle. Here, we consider three different scenarios defined by the aperture functions presented in 6) and (7).…”

Section: Exponential Barriersmentioning

confidence: 94%

“…The dotted green curve represents the scaled probability density of the free-particle Gaussian wave packet, 0.02 |Ψ free (x, t)| 2 , that would be observed in the absence of a barrier, i.e., for γ = 0. The effect of the barrier is to shift the transmitted wave packet by the distance ∆ ≃ −γσ 2 /v 0 with respect to the position of the freely evolved Gaussian [21]. Figure 4 shows the probability densities predicted by the AFM (solid red curve) and DPM (dash-dotted blue curve) for the barrier defined by χ(τ ) = min χ ∧ (τ ), 1 , with χ ∧ (τ ) ≡ cosh[γ(τ − t c )]/ cosh(γt c /2) and γ = 225 s −1 [see Fig.…”

Section: Exponential Barriersmentioning

confidence: 99%

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Comparison between two models of absorption of matter waves by a thin time-dependent barrier

Barbier¹,

Beau²,

Goussev³

2015

Phys. Rev. A

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We report a quantitative, analytical and numerical, comparison between two models of the interaction of a non-relativistic quantum particle with a thin time-dependent absorbing barrier. The first model represents the barrier by a set of time-dependent discontinuous matching conditions, which are closely related to Kottler boundary conditions used in stationary wave optics as a mathematical basis for Kirchhoff diffraction theory. The second model mimics the absorbing barrier with an off-diagonal δ-potential with a time-dependent amplitude. We show that the two models of absorption agree in their predictions in a semiclassical regime -the regime readily accessible in modern experiments with ultracold atoms.

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Section: Discussionmentioning

confidence: 85%

Section: Exponential Barriersmentioning

confidence: 94%

Section: Exponential Barriersmentioning

confidence: 99%

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Comparison between two models of absorption of matter waves by a thin time-dependent barrier

Barbier¹,

Beau²,

Goussev³

2015

Phys. Rev. A

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“…In quantum matter waves, the Moshinsky shutter or the sudden release of rectangular wave packet is also an example of sharp boundaries. The effects arising in the diffraction patterns due to non-sharp boundaries have been investigated recently [5,50,[70][71][72][73].…”

Section: Diffraction In Timementioning

confidence: 99%

Single-slit focusing and its representations

et al. 2017

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theory of light. Three years later he participated with his Mémoire sur la Diffraction de la Lumière in the Grand Prix of the French Academy of Sciences [2]. It was on this occasion that Siméon Poisson predicted that an opaque disc illuminated by parallel light would create a bright spot in the center of a shadow. This phenomenon was experimentally confirmed by Francois Arago and led to the victory of the wave over the particle theory. In the present article we discuss an effect related to the Poisson spot which is the onedimensional analogue of the camera obscura [3,4].Indeed, we have recently found [5] that a rectangular matter wave packet which undergoes free time evolution according to the Schrödinger equation focuses before it spreads. This phenomenon has been confirmed for light [6], water and surface plasmon waves [7]. In the present article we illustrate this effect in Wigner phase space and verify it using classical light in real space.Our article is organized as follows: in Sect. 2 we first give a brief history of the diffraction of waves, and then review several focusing effects especially those associated with the phenomenon of diffraction in time introduced in Moshinsky [8].We dedicate Sect. 3 to the discussion of the focusing of a rectangular wave packet from the point of view of the timedependent wave function. In particular, we show this effect Abstract We illustrate the phenomenon of the focusing of a freely propagating rectangular wave packet using three different tools: (1) the time-dependent wave function in position space, (2) the Wigner phase-space approach, and (3) an experiment using laser light.

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“…The expression (22) of K can now be used to construct the transmitted state Ψ(x, t). Indeed, substituting (10) and ( 22) into (15) yields the following expression of Ψ [38]:…”

Section: Modelmentioning

confidence: 99%

Phase-space representation of diffraction in time: Analytic results

Barbier,

Goussev

2021

Preprint

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Diffraction in time manifests itself as the appearance of probabilitydensity fringes when a matter wave passes through an opaque screen with abrupt temporal variation of transmission properties. Here we analytically describe the phasespace structure of diffraction-in-time fringes for a class of smooth time gratings. More precisely, we obtain an analytic expression for the Husimi distribution representing the state of the system in the case of time gratings comprising a succession of Lorentzianlike slits. In particular, for a double-slit scenario, we derive a simple and intuitive expression that accurately captures the position of interference fringes in phase space.

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Manipulating quantum wave packets via time-dependent absorption

Cited by 6 publications

References 34 publications

Comparison between two models of absorption of matter waves by a thin time-dependent barrier

Comparison between two models of absorption of matter waves by a thin time-dependent barrier

Single-slit focusing and its representations

Phase-space representation of diffraction in time: Analytic results

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