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Physical Review A

Double two-photon coalescence in a controlled propagation

Andrzej Raczyński, Jarosław Zaremba, Sylwia Zielińska‐Raczyńska

Published Mar 28, 2017• 2 citations
Publisher

Abstract

The propagation, storage, and release of two quantized light fields in an optically dressed atomic medium in the tripod configuration are studied. Using the formalism of spinor dark-state polaritons, the probabilities are obtained of finding outgoing photons of two possible localizations and two possible types, i.e., having different frequencies or polarizations. An additional interaction at the storage stage is applied which modifies the atomic coherences due to the stored photons; this results in a modification of the states of the outgoing photons. The conditions are examined for the photons' spatial and type coalescence typical of the Hong-Ou-Mandel effect, i.e., a zero probability of finding the outgoing photons having not only different localizations but also types. These results can possibly be observed in rubidium vapors.

DOI
10.1103/physreva.95.033836

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The propagation, storage, and release of two quantized light fields in an optically dressed atomic medium in the tripod configuration are studied. Using the formalism of spinor dark-state polaritons, the probabilities are obtained of finding outgoing photons of two possible localizations and two possible types, i.e., having different frequencies or polarizations. An additional interaction at the storage stage is applied which modifies the atomic coherences due to the stored photons; this results in a modification of the states of the outgoing photons. The conditions are examined for the photons' spatial and type coalescence typical of the Hong-Ou-Mandel effect, i.e., a zero probability of finding the outgoing photons having not only different localizations but also types. These results can possibly be observed in rubidium vapors.
Light propagation and storing in a medium of atoms in the tripod configuration driven by two control pulses are investigated theoretically in terms of two polaritons and numerically. It is shown that a magnetic field switched on at the pulse storage stage changes the phase relations between the atomic coherences due to the stored pulse, which leads to an essential modification of the released pulse. Quantitative relations concerning the released pulse and the coherences are given. A general situation when the two control fields are not proportional at the pulse release stage is also examined. It is shown that in both cases a single dark state polariton is not sufficient to account for the pulse evolution, which is connected with the fact that a part of the signal remains in the medium after the release stage.
We consider slow-light propagation in an atomic medium with a tripod level scheme. We show that the coexistence of two types of dark-state polaritons leads to the propagation dynamics, which is qualitatively different from that in a $\mathrm{\ensuremath{\Lambda}}$ medium, and allows therefore for very efficient conversion of signal photons into spin excitations. This efficiency is shown to be very close to 1 even for very long signal light pulses, which could not be entirely compressed into a $\mathrm{\ensuremath{\Lambda}}$ medium at a comparable strength of the control field.
It is shown that during light storage in an atomic medium in the $\mathrm{\ensuremath{\Lambda}}$ configuration, with not only the amplitude of the control field but also its phase changing adiabatically, a photon gains a Berry (geometric) phase. In the case of the tripod configuration with two probe fields the Berry phase is replaced by a $2\ifmmode\times\else\texttimes\fi{}2$ matrix. The probe fields are shown to be superpositions of two modes, each of them being characterized not only by its own velocity but also by its own Berry phase. If after light storage photons are released backwards, the contributions of the two modes interfere and the distribution of the outgoing photons can be steered by changing the difference between the Berry phases of the modes, due to the choice of the control field at the storage and release stages. In particular, one can turn a single photon of one of the probe fields into a photon of the other field or essentially modify coherent states of the incoming pulses.
Storing and release of a quantum light pulse in a medium of atoms in the tripod configuration are studied. Each of these operations is realized by switching on and off two sets of properly chosen control fields. The system constitutes a kind of a flexible beam splitter in which the input and output ports concern photons of the same direction but well separated in time. A version of Hong-Ou-Mandel interference is discussed. It is also shown that a stored nonclassical light is split into two nonclassical beams, with their statistical properties being steered by a choice of the control fields.
We investigate the storage of light in atomic rubidium vapor using a multilevel-tripod scheme. In the system, two collective dark polariton modes exist, forming an effective spinor quasiparticle. Storage of light is performed by dynamically reducing the optical group velocity to zero. After releasing the stored pulse, a beating of the two reaccelerated optical modes is monitored. The observed beating signal oscillates at an atomic transition frequency, opening the way to novel quantum limited measurements of atomic resonance frequencies and quantum switches.
We consider adiabatic propagation of a pair of quantized light pulses in a coherently prepared atomic medium with the tripod level configuration. We find that under conditions of electromagnetically induced transparency, two distinct polariton modes are simultaneously formed in the medium. These polaritons, represented by certain coherent superpositions of the quantized fields, have different group velocities; the fast one propagates at essentially the speed of light, while the group velocity of the slow polariton can be dynamically reduced to zero. The state mapping between the electromagnetic field and atomic ensemble is also demonstrated.