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Limit cycles and chaos in the hybrid atom-optomechanics system. Sci Rep 2022; 12:15288. [PMID: 36088462 PMCID: PMC9464193 DOI: 10.1038/s41598-022-15249-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2022] [Accepted: 06/21/2022] [Indexed: 11/17/2022] Open
Abstract
We consider atoms in two different periodic potentials induced by different lasers, one of which is coupled to a mechanical membrane via radiation pressure force. The atoms are intrinsically two-level systems that can absorb or emit photons, but the dynamics of their position and momentum are treated classically. On the other hand, the membrane, the cavity field, and the intrinsic two-level atoms are treated quantum mechanically. We show that the mean excitation of the three systems can be stable, periodically oscillating, or in a chaotic state depending on the strength of the coupling between them. We define regular, limit cycle, and chaotic phases, and present a phase diagram where the three phases can be achieved by manipulating the field-membrane and field-atom coupling strengths. We also computed other observable quantities that can reflect the system’s phase such as position, momentum, and correlation functions. Our proposal offers a new way to generate and tune the limit cycle and chaotic phases in a well-established atom-optomechanics system.
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2
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Dominici L, Voronova N, Colas D, Gianfrate A, Rahmani A, Ardizzone V, Ballarini D, De Giorgi M, Gigli G, Laussy FP, Sanvitto D. Shaping the topology of light with a moving Rabi-oscillating vortex. OPTICS EXPRESS 2021; 29:37262-37280. [PMID: 34808803 DOI: 10.1364/oe.438035] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2021] [Accepted: 10/13/2021] [Indexed: 06/13/2023]
Abstract
Quantum vortices are the analogue of classical vortices in optics, Bose-Einstein condensates, superfluids and superconductors, where they provide the elementary mode of rotation and orbital angular momentum. While they mediate important pair interactions and phase transitions in nonlinear fluids, their linear dynamics is useful for the shaping of complex light, as well as for topological entities in multi-component systems, such as full Bloch beams. Here, setting a quantum vortex into directional motion in an open-dissipative fluid of microcavity polaritons, we observe the self-splitting of the packet, leading to the trembling movement of its center of mass, whereas the vortex core undergoes ultrafast spiraling along diverging and converging circles, in a sub-picosecond precessing fashion. This singular dynamics is accompanied by vortex-antivortex pair creation and annihilation and a periodically changing topological charge. The spiraling and branching mechanics represent a direct manifestation of the underlying Bloch pseudospin space, whose mapping is shown to be rotating and splitting itself. Its reshaping is due to three simultaneous drives along the distinct directions of momentum and complex frequency, by means of the differential group velocities, Rabi frequency and dissipation rates, which are natural assets in coupled fields such as polaritons. This state, displaying linear momentum dressed with oscillating angular momentum, confirms the richness of multi-component and open quantum fluids and their innate potentiality to implement sophisticated and dynamical topological textures of light.
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3
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Bencheikh A, Chabou S, Boumeddine OC, Bekkis H, Benstiti A, Beddiaf L, Moussaoui W. Cosine beam: diffraction-free propagation and self-healing. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2020; 37:C7-C14. [PMID: 33175725 DOI: 10.1364/josaa.395940] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2020] [Accepted: 06/12/2020] [Indexed: 06/11/2023]
Abstract
In this paper we revisit the nondiffracting properties of the cosine beam (CB). Since the CB is of infinite extension and not physically realizable, we use two apodization pupils to manage its transverse extent: the first one is a Gaussian apodized pupil, giving rise to the cosine-Gauss (CG) beam, and the second one is a window (aperture) apodized pupil, giving rise to the cosine-windowed beam. Based on the second-order intensity moments, we demonstrate analytical expressions for the CG beam width and its nondiffracting range as a function of some key parameters. By considering the CG beam a standing wave resulting from the superposition of two oppositely oblique traveling Gaussian beams, we extend the study to higher-order CG beams. The latter is generated by the superposition of two oppositely oblique Hermite-Gauss (HGn) beams of order n, giving birth to a standing nondiffracting Hermite-cosine-Gauss (HCGn) beam of order n. We also demonstrate the expressions of the higher-order CG beam width and its nondiffracting range zmax. After demonstrating the nondiffracting nature of the HCG beam family, we test their ability to self-heal and recover against obstacles, and we show the limit distance from which HCGn beams self-heal as a function of obstruction size and CG parameter. The results of this paper are of big interest in fields involving structured light such as particle manipulation, imaging, and light sheet microscopy.
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4
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Simmons SA, Bayocboc FA, Pillay JC, Colas D, McCulloch IP, Kheruntsyan KV. What is a Quantum Shock Wave? PHYSICAL REVIEW LETTERS 2020; 125:180401. [PMID: 33196253 DOI: 10.1103/physrevlett.125.180401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2020] [Accepted: 08/20/2020] [Indexed: 06/11/2023]
Abstract
Shock waves are examples of the far-from-equilibrium behavior of matter; they are ubiquitous in nature, yet the underlying microscopic mechanisms behind their formation are not well understood. Here, we study the dynamics of dispersive quantum shock waves in a one-dimensional Bose gas, and show that the oscillatory train forming from a local density bump expanding into a uniform background is a result of quantum mechanical self-interference. The amplitude of oscillations, i.e., the interference contrast, decreases with the increase of both the temperature of the gas and the interaction strength due to the reduced phase coherence length. Furthermore, we show that vacuum and thermal fluctuations can significantly wash out the interference contrast, seen in the mean-field approaches, due to shot-to-shot fluctuations in the position of interference fringes around the mean.
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Affiliation(s)
- S A Simmons
- School of Mathematics and Physics, University of Queensland, Brisbane, Queensland 4072, Australia
| | - F A Bayocboc
- School of Mathematics and Physics, University of Queensland, Brisbane, Queensland 4072, Australia
| | - J C Pillay
- School of Mathematics and Physics, University of Queensland, Brisbane, Queensland 4072, Australia
| | - D Colas
- School of Mathematics and Physics, University of Queensland, Brisbane, Queensland 4072, Australia
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, University of Queensland, Brisbane, Queensland 4072, Australia
| | - I P McCulloch
- School of Mathematics and Physics, University of Queensland, Brisbane, Queensland 4072, Australia
| | - K V Kheruntsyan
- School of Mathematics and Physics, University of Queensland, Brisbane, Queensland 4072, Australia
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5
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Zakharko Y, Rother M, Graf A, Hähnlein B, Brohmann M, Pezoldt J, Zaumseil J. Radiative Pumping and Propagation of Plexcitons in Diffractive Plasmonic Crystals. NANO LETTERS 2018; 18:4927-4933. [PMID: 29995428 PMCID: PMC6089499 DOI: 10.1021/acs.nanolett.8b01733] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2018] [Revised: 06/24/2018] [Indexed: 05/26/2023]
Abstract
Strong coupling between plasmons and excitons leads to the formation of plexcitons: quasiparticles that combine nanoscale energy confinement and pronounced optical nonlinearities. In addition to these localized modes, the enhanced control over the dispersion relation of propagating plexcitons may enable coherent and collective coupling of distant emitters. Here, we experimentally demonstrate strong coupling between carbon nanotube excitons and spatially extended plasmonic modes formed via diffractive coupling of periodically arranged gold nanoparticles (nanodisks, nanorods). Depending on the light-matter composition, the rather long-lived plexcitons (>100 fs) undergo highly directional propagation over 20 μm. Near-field energy distributions calculated with the finite-difference time-domain method fully corroborate our experimental results. The previously demonstrated compatibility of this plexcitonic system with electrical excitation opens the path to the realization of a variety of ultrafast active plasmonic devices, cavity-assisted energy transport and low-power optoelectronic components.
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Affiliation(s)
- Yuriy Zakharko
- Institute
for Physical Chemistry, Universität
Heidelberg, D-69120 Heidelberg, Germany
| | - Marcel Rother
- Institute
for Physical Chemistry, Universität
Heidelberg, D-69120 Heidelberg, Germany
| | - Arko Graf
- Institute
for Physical Chemistry, Universität
Heidelberg, D-69120 Heidelberg, Germany
| | - Bernd Hähnlein
- Institut
für Mikro- und Nanotechnologie, Technische
Universität Ilmenau, 98693 Ilmenau, Germany
| | - Maximilian Brohmann
- Institute
for Physical Chemistry, Universität
Heidelberg, D-69120 Heidelberg, Germany
| | - Jörg Pezoldt
- Institut
für Mikro- und Nanotechnologie, Technische
Universität Ilmenau, 98693 Ilmenau, Germany
| | - Jana Zaumseil
- Institute
for Physical Chemistry, Universität
Heidelberg, D-69120 Heidelberg, Germany
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6
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Colas D, Laussy FP, Davis MJ. Negative-Mass Effects in Spin-Orbit Coupled Bose-Einstein Condensates. PHYSICAL REVIEW LETTERS 2018; 121:055302. [PMID: 30118304 DOI: 10.1103/physrevlett.121.055302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/27/2017] [Revised: 06/09/2018] [Indexed: 06/08/2023]
Abstract
Negative effective masses can be realized by engineering the dispersion relation of a variety of quantum systems. A recent experiment with spin-orbit coupled Bose-Einstein condensates has shown that a negative effective mass can halt the free expansion of the condensate and lead to fringes in the density [M. A. Khamehchi et al., Phys. Rev. Lett. 118, 155301 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.155301]. Here, we show that the underlying cause of these observations is the self-interference of the wave packet that arises when only one of the two effective mass parameters that characterize the dispersion of the system is negative. We show that spin-orbit coupled Bose-Einstein condensates may access regimes where both mass parameters controlling the propagation and diffusion of the condensate are negative, which leads to the novel phenomenon of counterpropagating self-interfering packets.
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Affiliation(s)
- David Colas
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, School of Mathematics and Physics, University of Queensland, St Lucia, Queensland 4072, Australia
| | - Fabrice P Laussy
- Faculty of Science and Engineering, University of Wolverhampton, Wulfruna Street, Wolverhampton WV1 1LY, United Kingdom
- Russian Quantum Center, Novaya 100, 143025 Skolkovo, Moscow Region, Russia
| | - Matthew J Davis
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, School of Mathematics and Physics, University of Queensland, St Lucia, Queensland 4072, Australia
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7
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Möhl C, Graf A, Berger FJ, Lüttgens J, Zakharko Y, Lumsargis V, Gather MC, Zaumseil J. Trion-Polariton Formation in Single-Walled Carbon Nanotube Microcavities. ACS PHOTONICS 2018; 5:2074-2080. [PMID: 29963582 PMCID: PMC6019025 DOI: 10.1021/acsphotonics.7b01549] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2017] [Indexed: 06/01/2023]
Abstract
We demonstrate the formation and tuning of charged trion-polaritons in polymer-sorted (6,5) single-walled carbon nanotubes in a planar metal-clad microcavity at room temperature. The positively charged trion-polaritons were induced by electrochemical doping and characterized by angle-resolved reflectance and photoluminescence spectroscopy. The doping level of the nanotubes within the microcavity was controlled by the applied bias and thus enabled tuning from mainly excitonic to a mixture of exciton and trion transitions. Mode splitting of more than 70 meV around the trion energy and emission from the new lower polariton branch corroborate a transition from exciton-polaritons (neutral) to trion-polaritons (charged). The estimated charge-to-mass ratio of these trion-polaritons is 200 times higher than that of electrons or holes in carbon nanotubes, which has exciting implications for the realization of polaritonic charge transport.
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Affiliation(s)
- Charles Möhl
- Institute
for Physical Chemistry, Universität
Heidelberg, D-69120 Heidelberg, Germany
| | - Arko Graf
- Institute
for Physical Chemistry, Universität
Heidelberg, D-69120 Heidelberg, Germany
| | - Felix J. Berger
- Institute
for Physical Chemistry, Universität
Heidelberg, D-69120 Heidelberg, Germany
| | - Jan Lüttgens
- Institute
for Physical Chemistry, Universität
Heidelberg, D-69120 Heidelberg, Germany
| | - Yuriy Zakharko
- Institute
for Physical Chemistry, Universität
Heidelberg, D-69120 Heidelberg, Germany
| | - Victoria Lumsargis
- Department
of Chemistry, Penn State University, University Park, Pennsylvania 16802, United States
| | - Malte C. Gather
- Organic
Semiconductor Centre, SUPA, School of Physics and Astronomy, University of St Andrews, St Andrews KY16 9SS, United Kingdom
| | - Jana Zaumseil
- Institute
for Physical Chemistry, Universität
Heidelberg, D-69120 Heidelberg, Germany
- Centre
for Advanced Materials, Universität
Heidelberg, D-69120 Heidelberg, Germany
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8
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Gianfrate A, Dominici L, Voronych O, Matuszewski M, Stobińska M, Ballarini D, De Giorgi M, Gigli G, Sanvitto D. Superluminal X-waves in a polariton quantum fluid. LIGHT, SCIENCE & APPLICATIONS 2018; 7:17119. [PMID: 30839621 PMCID: PMC6107045 DOI: 10.1038/lsa.2017.119] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2017] [Revised: 08/03/2017] [Accepted: 08/09/2017] [Indexed: 05/29/2023]
Abstract
In this work, we experimentally demonstrate for the first time the spontaneous generation of two-dimensional exciton-polariton X-waves. X-waves belong to the family of localized packets that can sustain their shape without spreading, even in the linear regime. This allows the wavepacket to maintain its shape and size for very low densities and very long times compared to soliton waves, which always necessitate a nonlinearity to compensate the diffusion. Here, we exploit the polariton nonlinearity and uniquely structured dispersion, comprising both positive- and negative-mass curvatures, to trigger an asymmetric four-wave mixing in momentum space. This ultimately enables the self-formation of a spatial X-wave front. Using ultrafast imaging experiments, we observe the early reshaping of the initial Gaussian packet into the X-pulse and its propagation, even for vanishingly small densities. This allows us to outline the crucial effects and parameters that drive the phenomena and to tune the degree of superluminal propagation, which we found to be in close agreement with numerical simulations.
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Affiliation(s)
- Antonio Gianfrate
- CNR NANOTEC, Istituto di Nanotecnologia, Via Monteroni, 73100 Lecce, Italy
| | - Lorenzo Dominici
- CNR NANOTEC, Istituto di Nanotecnologia, Via Monteroni, 73100 Lecce, Italy
| | - Oksana Voronych
- Institute of Theoretical Physics and Astrophysics, University of Gdańsk, ul. Wita Stwosza 57, 80-952 Gdańsk, Poland
| | - Michał Matuszewski
- Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
| | | | - Dario Ballarini
- CNR NANOTEC, Istituto di Nanotecnologia, Via Monteroni, 73100 Lecce, Italy
| | - Milena De Giorgi
- CNR NANOTEC, Istituto di Nanotecnologia, Via Monteroni, 73100 Lecce, Italy
| | - Giuseppe Gigli
- CNR NANOTEC, Istituto di Nanotecnologia, Via Monteroni, 73100 Lecce, Italy
| | - Daniele Sanvitto
- CNR NANOTEC, Istituto di Nanotecnologia, Via Monteroni, 73100 Lecce, Italy
- INFN, sezione di Lecce, 73100 Lecce, Italy
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9
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Ballarini D, Caputo D, Muñoz CS, De Giorgi M, Dominici L, Szymańska MH, West K, Pfeiffer LN, Gigli G, Laussy FP, Sanvitto D. Macroscopic Two-Dimensional Polariton Condensates. PHYSICAL REVIEW LETTERS 2017; 118:215301. [PMID: 28598653 DOI: 10.1103/physrevlett.118.215301] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2016] [Indexed: 06/07/2023]
Abstract
We report a record-size, two-dimensional polariton condensate of a fraction of a millimeter radius free from the presence of an exciton reservoir. This macroscopically occupied state is formed by the ballistically expanding polariton flow that relaxes and condenses over a large area outside of the excitation spot. The density of this trap-free condensate is <1 polariton/μm^{2}, reducing the phase noise induced by the interaction energy. Moreover, the backflow effect, recently predicted for the nonparabolic polariton dispersion, is observed here for the first time in the fast-expanding wave packet.
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Affiliation(s)
| | - Davide Caputo
- CNR NANOTEC-Istituto di Nanotecnologia, Via Monteroni, 73100 Lecce, Italy
- University of Salento, Via Arnesano, 73100 Lecce, Italy
| | | | - Milena De Giorgi
- CNR NANOTEC-Istituto di Nanotecnologia, Via Monteroni, 73100 Lecce, Italy
| | - Lorenzo Dominici
- CNR NANOTEC-Istituto di Nanotecnologia, Via Monteroni, 73100 Lecce, Italy
| | - Marzena H Szymańska
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Kenneth West
- PRISM, Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08540, USA
| | - Loren N Pfeiffer
- PRISM, Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08540, USA
| | - Giuseppe Gigli
- CNR NANOTEC-Istituto di Nanotecnologia, Via Monteroni, 73100 Lecce, Italy
- University of Salento, Via Arnesano, 73100 Lecce, Italy
| | - Fabrice P Laussy
- University of Wolverhampton, Faculty of Science & Engineering, Wulfruna Street, Wolverhampton WV1 1LY, United Kingdom
- Russian Quantum Center, Novaya 100, 143025 Skolkovo, Moscow Region, Russia
| | - Daniele Sanvitto
- CNR NANOTEC-Istituto di Nanotecnologia, Via Monteroni, 73100 Lecce, Italy
- INFN, Sezione di Lecce, 73100 Lecce, Italy
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10
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Pinsker F, Ruan X, Alexander TJ. Effects of the non-parabolic kinetic energy on non-equilibrium polariton condensates. Sci Rep 2017; 7:1891. [PMID: 28507290 PMCID: PMC5432531 DOI: 10.1038/s41598-017-01113-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2016] [Accepted: 03/22/2017] [Indexed: 11/09/2022] Open
Abstract
In the study of non-equilibrium polariton condensates it is usually assumed that the dispersion relation of polaritons is parabolic in nature. We show that considering the true non-parabolic kinetic energy of polaritons leads to significant changes in the behaviour of the condensate due to the curvature of the dispersion relation and the possibility of transfer of energy to high wavenumber components in the condensate spatial profile. We present explicit solutions for plane waves and linear excitations, and identify the differences in the theoretical predictions between the parabolic and non-parabolic mean-field models, showing the possibility of symmetry breaking in the latter. We then consider the evolution of wavepackets and show that self-localisation effects may be observed due to the curvature of the dispersion relation. Finally, we revisit the dynamics of dark soliton trains and show that additional localized density excitations may emerge in the dynamics due to the excitation of high frequency components, mimicking the appearance of near-bright solitary waves over short timescales.
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Affiliation(s)
- F Pinsker
- Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU, United Kingdom.
| | - X Ruan
- Department of Mathematics, National University of Singapore, Singapore, Singapore
| | - T J Alexander
- School of Physical, Environmental and Mathematical Sciences, UNSW Canberra, Canberra ACT, 2600, Australia
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11
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Rahmani A, Laussy FP. Polaritonic Rabi and Josephson Oscillations. Sci Rep 2016; 6:28930. [PMID: 27452872 PMCID: PMC4958973 DOI: 10.1038/srep28930] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2016] [Accepted: 06/07/2016] [Indexed: 11/08/2022] Open
Abstract
The dynamics of coupled condensates is a wide-encompassing problem with relevance to superconductors, BECs in traps, superfluids, etc. Here, we provide a unified picture of this fundamental problem that includes i) detuning of the free energies, ii) different self-interaction strengths and iii) finite lifetime of the modes. At such, this is particularly relevant for the dynamics of polaritons, both for their internal dynamics between their light and matter constituents, as well as for the more conventional dynamics of two spatially separated condensates. Polaritons are short-lived, interact only through their material fraction and are easily detuned. At such, they bring several variations to their atomic counterpart. We show that the combination of these parameters results in important twists to the phenomenology of the Josephson effect, such as the behaviour of the relative phase (running or oscillating) or the occurence of self-trapping. We undertake a comprehensive stability analysis of the fixed points on a normalized Bloch sphere, that allows us to provide a generalized criterion to identify the Rabi and Josephson regimes in presence of detuning and decay.
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Affiliation(s)
- Amir Rahmani
- Physics Department, Yazd University, P.O. Box
89195-741, Yazd, Iran
| | - Fabrice P. Laussy
- Russian Quantum Center, Novaya 100,
143025
Skolkovo, Moscow Region, Russia
- Condensed Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, E-28049, Spain
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