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Ji K, Zhong Q, Ge L, Beaudoin G, Sagnes I, Raineri F, El-Ganainy R, Yacomotti AM. Tracking exceptional points above the lasing threshold. Nat Commun 2023; 14:8304. [PMID: 38097572 PMCID: PMC10721897 DOI: 10.1038/s41467-023-43874-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2023] [Accepted: 11/22/2023] [Indexed: 12/17/2023] Open
Abstract
Recent studies on exceptional points (EPs) in non-Hermitian optical systems have revealed unique traits, including unidirectional invisibility, chiral mode switching and laser self-termination. In systems featuring gain/loss components, EPs are commonly accessed below the lasing threshold, i.e., in the linear regime. In this work, we experimentally demonstrate that EP singularities in coupled semiconductor nanolasers can be accessed above the lasing threshold, where they become branch points of a nonlinear dynamical system. Contrary to the common belief that unavoidable cavity detuning impedes the formation of EPs, here we demonstrate that such detuning is necessary for compensating the carrier-induced frequency shift, hence restoring the EP. Furthermore, we find that the pump imbalance at lasing EPs varies with the total pump power, enabling their continuous tracking. This work uncovers the unstable nature of EPs above laser threshold in coupled semiconductor lasers, offering promising opportunities for the realization of self-pulsing nanolaser devices and frequency combs.
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Affiliation(s)
- Kaiwen Ji
- Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Saclay, 10 Boulevard Thomas Gobert, 91120, Palaiseau, France
| | - Qi Zhong
- Department of Physics, Michigan Technological University, Houghton, Michigan, 49931, USA
| | - Li Ge
- Department of Physics and Astronomy, College of Staten Island, CUNY, Staten Island, New York, 10314, USA
- Graduate Center, CUNY, New York, New York, 10016, USA
| | - Gregoire Beaudoin
- Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Saclay, 10 Boulevard Thomas Gobert, 91120, Palaiseau, France
| | - Isabelle Sagnes
- Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Saclay, 10 Boulevard Thomas Gobert, 91120, Palaiseau, France
| | - Fabrice Raineri
- Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Saclay, 10 Boulevard Thomas Gobert, 91120, Palaiseau, France
| | - Ramy El-Ganainy
- Department of Physics, Michigan Technological University, Houghton, Michigan, 49931, USA.
- Henes Center for Quantum Phenomena, Michigan Technological University, Houghton, Michigan, 49931, USA.
| | - Alejandro M Yacomotti
- Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Saclay, 10 Boulevard Thomas Gobert, 91120, Palaiseau, France.
- LP2N, Institut d'Optique Graduate School, CNRS, Université de Bordeaux, 33400, Talence, France.
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Zheng X, Dolde J, Cambria MC, Lim HM, Kolkowitz S. A lab-based test of the gravitational redshift with a miniature clock network. Nat Commun 2023; 14:4886. [PMID: 37573452 PMCID: PMC10423269 DOI: 10.1038/s41467-023-40629-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2023] [Accepted: 08/03/2023] [Indexed: 08/14/2023] Open
Abstract
Einstein's theory of general relativity predicts that a clock at a higher gravitational potential will tick faster than an otherwise identical clock at a lower potential, an effect known as the gravitational redshift. Here we perform a laboratory-based, blinded test of the gravitational redshift using differential clock comparisons within an evenly spaced array of 5 atomic ensembles spanning a height difference of 1 cm. We measure a fractional frequency gradient of [ - 12.4 ± 0. 7(stat) ± 2. 5(sys)] × 10-19/cm, consistent with the expected redshift gradient of - 10.9 × 10-19/cm. Our results can also be viewed as relativistic gravitational potential difference measurements with sensitivity to mm scale changes in height on the surface of the Earth. These results highlight the potential of local-oscillator-independent differential clock comparisons for emerging applications of optical atomic clocks including geodesy, searches for new physics, gravitational wave detection, and explorations of the interplay between quantum mechanics and gravity.
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Affiliation(s)
- Xin Zheng
- Department of Physics, University of Wisconsin-Madison, Madison, WI, 53706, USA
| | - Jonathan Dolde
- Department of Physics, University of Wisconsin-Madison, Madison, WI, 53706, USA
| | - Matthew C Cambria
- Department of Physics, University of Wisconsin-Madison, Madison, WI, 53706, USA
| | - Hong Ming Lim
- Department of Physics, University of Wisconsin-Madison, Madison, WI, 53706, USA
| | - Shimon Kolkowitz
- Department of Physics, University of Wisconsin-Madison, Madison, WI, 53706, USA.
- Department of Physics, University of California, Berkeley, CA, 94720, USA.
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Savary L. Quantum loop states in spin-orbital models on the honeycomb lattice. Nat Commun 2021; 12:3004. [PMID: 34021135 PMCID: PMC8139991 DOI: 10.1038/s41467-021-23033-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2017] [Accepted: 04/05/2021] [Indexed: 11/09/2022] Open
Abstract
The search for truly quantum phases of matter is a center piece of modern research in condensed matter physics. Quantum spin liquids, which host large amounts of entanglement-an entirely quantum feature where one part of a system cannot be measured without modifying the rest-are exemplars of such phases. Here, we devise a realistic model which relies upon the well-known Haldane chain phase, i.e. the phase of spin-1 chains which host fractional excitations at their ends, akin to the hallmark excitations of quantum spin liquids. We tune our model to exactly soluble points, and find that the ground state realizes Haldane chains whose physical supports fluctuate, realizing both quantum spin liquid like and symmetry-protected topological phases. Crucially, this model is expected to describe actual materials, and we provide a detailed set of material-specific constraints which may be readily used for an experimental realization.
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Affiliation(s)
- Lucile Savary
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA.
- Université de Lyon, École Normale Supérieure de Lyon, Université Claude Bernard Lyon I, CNRS, Laboratoire de physique, Lyon, France.
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