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Journal of the Optical Society of America B

Controlling parameters of the wave-particle duality of a two-level atom in a double-slit scheme with cavity field

Mario Miranda, Miguel Orszag

Published Jan 5, 2021• 0 citations
Publisher

Abstract

A double-slit scheme placed immediately before a standing wave allows one to establish two possible paths for the passage of an atom. Each path matches with a node or antinode of the wave. The atom–field interaction is maximum (null) when the atom crosses an antinode (node), causing a maximum (null) phase shift in the field. Therefore, after the interaction, a proper quadrature measurement on the field can reveal the value of its final phase, and which-path information can be obtained. For a coherent state, the which-path information can be controlled by the amplitude of the field, and partial interference can be observed as it decreases. In this paper, we consider different states of the quantum field (squeezed coherent, cat, and thermal states), and we establish correlations between the internal atomic states and the paths of the double-slit scheme. This allows us to study the relationship among visibility, distinguishability, and concurrence, having in both the field and the atom different controlling parameters of the wave-particle duality.

DOI
10.1364/josab.411761

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A double-slit scheme placed immediately before a standing wave allows one to establish two possible paths for the passage of an atom. Each path matches with a node or antinode of the wave. The atom–field interaction is maximum (null) when the atom crosses an antinode (node), causing a maximum (null) phase shift in the field. Therefore, after the interaction, a proper quadrature measurement on the field can reveal the value of its final phase, and which-path information can be obtained. For a coherent state, the which-path information can be controlled by the amplitude of the field, and partial interference can be observed as it decreases. In this paper, we consider different states of the quantum field (squeezed coherent, cat, and thermal states), and we establish correlations between the internal atomic states and the paths of the double-slit scheme. This allows us to study the relationship among visibility, distinguishability, and concurrence, having in both the field and the atom different controlling parameters of the wave-particle duality.
A double-cavity with a quantum mechanical and a classical field is placed immediately behind a double-slit in order to analyze the wave-particle duality. Both fields have common nodes and antinodes through which a three-level atom passes after crossing the double-slit. The atom-field interaction is maximum when the atom crosses a common antinode and path information can be recorded on the phase of the quantum field. On the other hand, if the atom crosses a common node, the interaction is null and no path information is stored. A quadrature measurement on the quantum field can reveal the path followed by the atom, depending on its initial amplitude $\ensuremath{\alpha}$ and the classical amplitude $\ensuremath{\varepsilon}$. In this report we show that the classical radiation acts like a focusing element of the interference and diffraction patterns and how it alters the visibility and distinguishabilily. Furthermore, in our double-slit scheme the two possible paths are correlated with the internal atomic states, which allows us to study the relationship between concurrence and wave-particle duality considering different cases.
A double cavity with a quantum mechanical and a classical field is located immediately behind of a double-slit in order to analyse the wave-particle duality. Both fields have common nodes and antinodes through which a three-level atom passes after crossing the double-slit. The atom-field interaction is maximum when the atom crosses a common antinode and path-information can be recorded on the phase of the quantum field. On other hand, if the atom crosses a common node, the interaction is null and no path-information is stored. A quadrature measurement on the quantum field can reveal the path followed by the atom, depending on its initial amplitude ααα and the classical amplitude ε\varepsilonε. In this report we show that the classical radiation acts like a focusing element of the interference and diffraction patterns and how it alters the visibility and distinguishabilily. Furthermore, in our double-slit scheme the two possible paths are correlated with the internal atomic states, which allows us to study the relationship between concurrence and wave-particle duality considering different cases.
We propose for the experimental verification of an inequality concerning wave-particle duality by Englert [Phys. Rev. Lett. 77, 2154 (1996)] relating (or setting) an upper limit on distinguishability and visibility in a two-way interferometer. The inequality, quantifies the concept of wave-particle duality. The considered two-way interferometer is a Young's double-slit experiment involving two four-level atoms and is a slightly modified version of that of the recent experiment by Eichmann et al. [Phys. Rev. Lett. 70, 2359 (1993)]. The fringe visibility depends on the detected polarization direction of the scattered light and a read out of the internal state of one of the two atoms provides a partial which-way information.
According to the relevant theories on duality relation, the summation of the extractable information of a quanton’s wave and particle properties, which are characterized by interference visibility V and path distinguishability D, respectively, is limited. However, this relation is violated upon quantum superposition between the wave-state and particle-state of the quanton, which is caused by the quantum beamsplitter (QBS). Along another line, recent studies have considered quantum coherence C in the l1-norm measure as a candidate for the wave property. In this study, we propose an interferometer with a quantum which-path detector (QWPD) and examine the generalized duality relation based on C. We find that this relationship still holds under such a circumstance, but the interference between these two properties causes the full-particle property to be observed when the QWPD system is partially present. Using a pair of polarization-entangled photons, we experimentally verify our analysis in the two-path case. This study extends the duality relation between coherence and path information to the quantum case and reveals the effect of quantum superposition on the duality relation.
The "welcher Weg" (which-path) detector as described by Scully et al. [Nature 351, 111 (1991)] employs a pair of initially empty micromaser cavities placed in front of a double-slit apparatus in an atomic interferometer. Laser excited atoms spontaneously emit a photon into either cavity thereby marking the atoms' path and thereby destroying the interference. I propose an alternative method wherein at least one of the cavities is prepared in a coherent state with a strong amplitude. Which-path information is obtained by a nonresonant, dispersive type of atom-field interaction associated with quantum nondemolition measurements. Ground-state atoms passing through the cavity remain in the ground state but impart a phase shift to the cavity fields. Velocity selection is shown to affect the visibility of the fringes. An associated quantum eraser is also discussed.
Complementarity, a fundamental tenet of quantum optics, is indispensable for elucidating the fundamental principles of quantum physics and advancing quantum information processing applications. In the context of wave–particle duality, induced-coherence experiments were understood through the lens of which-path information. Conversely, the stimulated-coherence experiments were explained by using the indistinguishability of the photon statistics of conjugate photons as a means of realizing complementarity. Here, we report a systematic approach for establishing a complementary relationship between the interference visibility, concurrence, and predictability in the crossing of induced and stimulated coherences of two-mode squeezed coherent states. This is achieved using a double-path interferometer involving two independent four-wave mixing (FWM) atomic samples generated via spontaneous and stimulated FWM processes from a warm atomic ensemble of 87 Rb. We demonstrate that the transition from quantum to classical behavior can be characterized by the induced coherence effect, distinguishing between the two-mode squeezed vacuum and coherent states. Moreover, our experimental scheme, employing two FWM atomic ensembles with long-coherent photons, provides valuable insights into the complementarity of which-path information in induced and stimulated coherences.