Goldstone mode of optical parametric oscillators in planar semiconductor microcavities in the strong-coupling regime
Abstract
We propose an experimental setup to probe the low-lying excitation modes of a parametrically oscillating planar cavity, in particular the soft Goldstone mode which appears as a consequence of the spontaneously broken $\text{U}(1)$ symmetry of signal-idler phase rotations. A strong and narrow peak corresponding to the Goldstone mode is identified in the transmission spectrum of a weak probe beam incident on the cavity. When the $\text{U}(1)$ symmetry is explicitly broken by an additional laser beam pinning the signal-idler phase, a gap opens in the dispersion and the Goldstone peak is dramatically suppressed. Quantitative predictions are given for the case of semiconductor planar cavities in the strong exciton-photon coupling regime.
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While particle-number conservation makes it difficult to verify this prediction in atomic condensates at equilibrium, the phase of an optical condensate can be pinned by an additional incident coherent laser, and a clear gap in the Goldstone mode dispersion is observed in experiments.
“While particle-number conservation makes it difficult to verify this prediction in atomic condensates at equilibrium [124], the phase of an optical condensate can be pinned by an additional incident coherent laser [125] and a clear gap in the Goldstone mode dispersion is clearly observed in experiments [106].”
From How to exploit driving and dissipation to stabilize and manipulate quantum many-body states (2025) · cites this paper as [125]
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Self-citationObservation of the diffusive Nambu–Goldstone mode of a non-equilibrium phase transition
Claude, F., Jacquet, M. J., Glorieux, Q., Wouters, M., Giacobino, E., Carusotto, I., & Bramati, A. (2025) · Nature Physics · doi:10.1038/s41567-025-02902-z · Cited by 7 · see citing works
“Although the idealized theory of the NG mode for a spatially infinite system and a perturbatively weak probe 22,23,42 , illustrated in the numerical simulations of Fig.”
InfluentialSelf-citationHow to exploit driving and dissipation to stabilize and manipulate quantum many-body states
Carusotto, I. (2025) · Comptes Rendus. Physique · doi:10.5802/crphys.258 · Cited by 5 · see citing works
“The optical analog of this idea was investigated in [83, 97]: the phase of a condensate can be pinned by an additional incident coherent field.”
Self-citation
- Authors
- Wouters, M., & Carusotto, I.
- Affiliations
- University of Antwerp (BE)
- University of Trento (IT)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2007-10-09
- Volume
- 76
- Issue
- 4
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1966994032
- Cited by
- 79
- References
- 0
- Citations by year
- 2026: 4 · 2025: 6 · 2024: 1 · 2023: 4 · 2022: 5 · 2021: 1 · 2020: 4 · 2018: 4 · 2017: 4 · 2016: 3 · 2015: 5 · 2014: 4 · 2013: 6 · 2012: 9
- FWCI
- 3.26
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review A (publishedVersion)
- Institutional Research Information System (Università degli Studi di Trento) (submittedVersion)
- Funders
- European Commission
- Bundesministerium für Bildung und Forschung
- Fonds Wetenschappelijk Onderzoek
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Strong Light-Matter Interactions
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Photorefractive and Nonlinear Optics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum optics and atomic interactions
- Keywords
- Goldstone modes, optical parametric oscillator, U(1) symmetry breaking, spontaneous symmetry breaking, transmission spectra, probe beam
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