1
|
Loughlin HA, Sudhir V. Quantum noise and its evasion in feedback oscillators. Nat Commun 2023; 14:7083. [PMID: 37925495 PMCID: PMC10625586 DOI: 10.1038/s41467-023-42739-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2023] [Accepted: 10/20/2023] [Indexed: 11/06/2023] Open
Abstract
Feedback oscillators, consisting of an amplifier whose output is partially fed back to its input, provide stable references for standardization and synchronization. Notably, the laser is such an oscillator whose performance can be limited by quantum fluctuations. The resulting frequency instability, quantified by the Schawlow-Townes formula, sets a limit to laser linewidth. Here, we show that the Schawlow-Townes formula applies universally to feedback oscillators beyond lasers. This is because it arises from quantum noise added by the amplifier and out-coupler in the feedback loop. Tracing the precise origin of quantum noise in an oscillator informs techniques to systematically evade it: we show how squeezing and entanglement can enable sub-Schawlow-Townes linewidth feedback oscillators. Our analysis clarifies the quantum limits to the stability of feedback oscillators in general, derives a standard quantum limit (SQL) for all such devices, and quantifies the efficacy of quantum strategies in realizing sub-SQL oscillators.
Collapse
Affiliation(s)
- Hudson A Loughlin
- LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
| | - Vivishek Sudhir
- LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
| |
Collapse
|
2
|
Abstract
Optical vortices are beams of laser light with screw symmetry in their wavefront. With a corresponding azimuthal dependence in optical phase, they convey orbital angular momentum, and their methods of production and applications have become one of the most rapidly accelerating areas in optical physics and technology. It has been established that the quantum nature of electromagnetic radiation extends to properties conveyed by each individual photon in such beams. It is therefore of interest to identify and characterize the symmetry aspects of the quantized fields of vortex radiation that relate to the beam and become manifest in its interactions with matter. Chirality is a prominent example of one such aspect; many other facets also invite attention. Fundamental CPT symmetry is satisfied throughout the field of optics, and it plays significantly into manifestations of chirality where spatial parity is broken; duality symmetry between electric and magnetic fields is also involved in the detailed representation. From more specific considerations of spatial inversion, amongst which it emerges that the topological charge has the character of a pseudoscalar, other elements of spatial symmetry, beyond simple parity inversion, prove to repay additional scrutiny. A photon-based perspective on these features enables regard to be given to the salient quantum operators, paying heed to quantum uncertainty limits of observables. The analysis supports a persistence in features of significance for the material interactions of vortex beams, which may indicate further scope for suitably tailored experimental design.
Collapse
|
3
|
|
4
|
Luis A. Nonclassical light revealed by the joint statistics of simultaneous measurements. OPTICS LETTERS 2016; 41:1789-1792. [PMID: 27082346 DOI: 10.1364/ol.41.001789] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Nonclassicality cannot be a single-observable property, since the statistics of any quantum observable is compatible with classical physics. We develop a general procedure to reveal nonclassical behavior of light states from the joint statistics arising in the practical measurement of multiple observables. Beside embracing previous approaches, this protocol can disclose nonclassical features for standard examples of classical-like behavior, such as SU(2) and Glauber coherent states. When combined with other criteria, this would imply that every light state is nonclassical.
Collapse
|
5
|
Lee C, Alexander TJ, Kivshar YS. Melting of discrete vortices via quantum fluctuations. PHYSICAL REVIEW LETTERS 2006; 97:180408. [PMID: 17155525 DOI: 10.1103/physrevlett.97.180408] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2006] [Indexed: 05/12/2023]
Abstract
We consider nonlinear boson states with a nontrivial phase structure in the three-site Bose-Hubbard ring, quantum discrete vortices (or q vortices), and study their "melting" under the action of quantum fluctuations. We calculate the spatial correlations in the ground states to show the superfluid-insulator crossover and analyze the fidelity between the exact and variational ground states to explore the validity of the classical analysis. We examine the phase coherence and the effect of quantum fluctuations on q vortices and reveal that the breakdown of these coherent structures through quantum fluctuations accompanies the superfluid-insulator crossover.
Collapse
Affiliation(s)
- Chaohong Lee
- Nonlinear Physics Centre and ARC Centre of Excellence for Quantum-Atom Optics, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia
| | | | | |
Collapse
|
6
|
Al-Kader GMA. Phase distribution from the Wigner function for superpositions of squeezed displaced Fock states. JOURNAL OF OPTICS B: QUANTUM AND SEMICLASSICAL OPTICS 2003; 5:S228-S232. [DOI: 10.1088/1464-4266/5/3/352] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
|
7
|
Al-Kader GMA. Linear Amplifier and the Coherent States Superpositions. PHYSICA SCRIPTA 2001; 63:372-378. [DOI: 10.1238/physica.regular.063a00372] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
|
8
|
Al-Kader GMA. Linear amplifier via the squeezed coherent states superpositions. ACTA PHYSICA SINICA (OVERSEAS EDITION) 1999; 8:754-767. [DOI: 10.1088/1004-423x/8/10/005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
|
9
|
|
10
|
|
11
|
Jaekel MT, Reynaud S. Time-frequency transfer with quantum fields. PHYSICAL REVIEW LETTERS 1996; 76:2407-2411. [PMID: 10060692 DOI: 10.1103/physrevlett.76.2407] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
12
|
Luis A, Sánchez-Soto LL. Probability distributions for the phase difference. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1996; 53:495-501. [PMID: 9912907 DOI: 10.1103/physreva.53.495] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
13
|
Vaccaro J. Number-phase Wigner function on Fock space. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1995; 52:3474-3488. [PMID: 9912647 DOI: 10.1103/physreva.52.3474] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
14
|
Ficek Z, Dalton BJ, Knight PL. Fluorescence intensity and squeezing in a driven three-level atom: Ladder case. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1995; 51:4062-4077. [PMID: 9912081 DOI: 10.1103/physreva.51.4062] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
15
|
Vaccaro JA. Phase operators on Hilbert space. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1995; 51:3309-3317. [PMID: 9911970 DOI: 10.1103/physreva.51.3309] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
16
|
Luis A, Sánchez-Soto LL, Tanas R. Phase properties of light propagating in a Kerr medium: Stokes parameters versus Pegg-Barnett predictions. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1995; 51:1634-1643. [PMID: 9911752 DOI: 10.1103/physreva.51.1634] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
17
|
Leonhardt U, Vaccaro JA, Böhmer B, Paul H. Canonical and measured phase distributions. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1995; 51:84-95. [PMID: 9911559 DOI: 10.1103/physreva.51.84] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
18
|
Kuang LM, Chen X. Phase-coherent states and their squeezing properties. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1994; 50:4228-4236. [PMID: 9911396 DOI: 10.1103/physreva.50.4228] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
19
|
Dalton BJ, Ficek Z, Knight PL. Optimum field squeezing from atomic sources: Three-level atoms. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1994; 50:2646-2666. [PMID: 9911186 DOI: 10.1103/physreva.50.2646] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
20
|
Riegler P, Wódkiewicz K. Phase-space representation of operational phase operators. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1994; 49:1387-1391. [PMID: 9910372 DOI: 10.1103/physreva.49.1387] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
21
|
Luis A, Sánchez-Soto LL. Phase-difference operator. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1993; 48:4702-4708. [PMID: 9910179 DOI: 10.1103/physreva.48.4702] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
22
|
Noh JW, Fougères A, Mandel L. Measurements of the probability distribution of the operationally defined quantum phase difference. PHYSICAL REVIEW LETTERS 1993; 71:2579-2582. [PMID: 10054717 DOI: 10.1103/physrevlett.71.2579] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
23
|
Schieve WC, McGowan RR. Phase distribution and linewidth in the micromaser. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1993; 48:2315-2323. [PMID: 9909855 DOI: 10.1103/physreva.48.2315] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
24
|
Luis A, Sánchez-Soto LL. Canonical transformations to action and phase-angle variables and phase operators. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1993; 48:752-757. [PMID: 9909651 DOI: 10.1103/physreva.48.752] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
25
|
Barnett SM, Pegg DT. Phase measurements. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1993; 47:4537-4540. [PMID: 9909470 DOI: 10.1103/physreva.47.4537] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
26
|
Luis A, Sánchez-Soto LL. Alternative derivation of the Pegg-Barnett phase operator. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1993; 47:1492-1496. [PMID: 9909073 DOI: 10.1103/physreva.47.1492] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
27
|
Burak D, Wódkiewicz K. Phase properties of quantum states of light. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 46:2744-2748. [PMID: 9908434 DOI: 10.1103/physreva.46.2744] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
28
|
Noh JW, Fougères A, Mandel L. Further investigations of the operationally defined quantum phase. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 46:2840-2852. [PMID: 9908444 DOI: 10.1103/physreva.46.2840] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
29
|
Luks A, Perinová V, Krepelka J. Special states of the plane rotator relevant to the light field. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 46:489-498. [PMID: 9907888 DOI: 10.1103/physreva.46.489] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
30
|
Buzek V, Wilson-Gordon AD, Knight PL, Lai WK. Coherent states in a finite-dimensional basis: Their phase properties and relationship to coherent states of light. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 45:8079-8094. [PMID: 9906903 DOI: 10.1103/physreva.45.8079] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
31
|
Noh JW, Fougères A, Mandel L. Operational approach to the phase of a quantum field. PHYSICAL REVIEW A 1992; 45:424-442. [PMID: 9906741 DOI: 10.1103/physreva.45.424] [Citation(s) in RCA: 69] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
32
|
Vogel W, Schleich W. Phase distribution of a quantum state without using phase states. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 44:7642-7646. [PMID: 9905903 DOI: 10.1103/physreva.44.7642] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
33
|
Noh JW, Fougères A, Mandel L. Measurement of the quantum phase by photon counting. PHYSICAL REVIEW LETTERS 1991; 67:1426-1429. [PMID: 10044144 DOI: 10.1103/physrevlett.67.1426] [Citation(s) in RCA: 77] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
34
|
Gantsog T, Tanas R. Phase properties of a damped anharmonic oscillator. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 44:2086-2093. [PMID: 9906177 DOI: 10.1103/physreva.44.2086] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
35
|
Meystre P, Slosser J, Wilkens M. Cotangent states of the electromagnetic field: Squeezing and phase properties. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 43:4959-4964. [PMID: 9905614 DOI: 10.1103/physreva.43.4959] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
36
|
Ma X, Rhodes W. Comment on "Phase properties of the quantized single-mode electromagnetic field". PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 43:2576-2578. [PMID: 9905315 DOI: 10.1103/physreva.43.2576] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
|
37
|
Barnett SM, Pegg DT. Quantum theory of optical phase correlations. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 42:6713-6720. [PMID: 9903971 DOI: 10.1103/physreva.42.6713] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
38
|
Gerry CC, Urbanski KE. Hermitian phase-difference operator analysis of microscopic radiation-field measurements. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 42:662-664. [PMID: 9903851 DOI: 10.1103/physreva.42.662] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
39
|
Vaccaro JA, Pegg DT. Wigner function for number and phase. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 41:5156-5163. [PMID: 9903742 DOI: 10.1103/physreva.41.5156] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
40
|
Barnett SM, Pegg DT. Quantum theory of rotation angles. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 41:3427-3435. [PMID: 9903510 DOI: 10.1103/physreva.41.3427] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
41
|
Lynch R. Fluctuation of the Barnett-Pegg phase operator in a coherent state. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 41:2841-2843. [PMID: 9903419 DOI: 10.1103/physreva.41.2841] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
42
|
Pegg DT, Barnett SM. Phase properties of the quantized single-mode electromagnetic field. PHYSICAL REVIEW. A, GENERAL PHYSICS 1989; 39:1665-1675. [PMID: 9901420 DOI: 10.1103/physreva.39.1665] [Citation(s) in RCA: 168] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
43
|
|
44
|
Dupertuis MA. Alternate orderings: A new tool for the study of phase and photon statistics. PHYSICAL REVIEW. A, GENERAL PHYSICS 1988; 37:4752-4764. [PMID: 9899623 DOI: 10.1103/physreva.37.4752] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|