Quantum Noise Theory of Exceptional Point Amplifying Sensors

Zhang, Mengzhen; Sweeney, William R.; Hsu, Chia Wei; Yang, Lan; Stone, A. Douglas; Jiang, Liang

doi:10.1103/physrevlett.123.180501

Cited by 218 publications

(155 citation statements)

References 40 publications

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“…The advantages of EPs for applications remain a very active topic of research [16,[59][60][61][62][63][64][65][66][67][68][69][70][71][72] and correctly modelling noise and quantum jumps is fundamental to correctly adress the question of, e.g., EPs sensitivity. We believe that our work, showing explicitly the operational interpretation and the relation between classical and quantum EPs in terms of postselection and/or inefficient detectors, can stimulate more interest in experimental demonstrations of LEPs and their potential quantum applications, pointing out analogies and differences with respect to those studied for semiclassical HEPs.…”

Section: Discussionmentioning

confidence: 99%

Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps

et al. 2019

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Exceptional points (EPs) are degeneracies of classical and quantum open systems, which are studied in many areas of physics including optics, optoelectronics, plasmonics, and condensed matter physics. In the semiclassical regime, open systems can be described by phenomenological effective non-Hermitian Hamiltonians (NHHs) capturing the effects of gain and loss in terms of imaginary fields. The EPs that characterize the spectra of such Hamiltonians (HEPs) describe the time evolution of a system without quantum jumps. It is well known that a full quantum treatment describing more generic dynamics must crucially take into account such quantum jumps. In a recent paper [Minganti et al., Phys. Rev. A 100, 062131 (2019)], we generalized the notion of EPs to the spectra of Liouvillian superoperators governing open system dynamics described by Linblad master equations. Intriguingly, we found that in situations where a classical to quantum correspondence exists, the two types of dynamics can yield different EPs. In a recent experimental work [Naghiloo et al. Nat. Phys. 15, 1232(2019], it was shown that one can engineer a non-Hermitian Hamiltonian in the quantum limit by postselecting on certain quantum jump trajectories. This raises an interesting question concerning the relation between Hamiltonian and Lindbladian EPs, and quantum trajectories. We discuss these connections by introducing a hybrid-Liouvillian superoperator, capable of describing the passage from an NHH (when one postselects only those trajectories without quantum jumps) to a true Liouvillian including quantum jumps (without postselection). Beyond its fundamental interest, our approach allows to efficiently discuss and analyze postselection on finite-efficiency detectors. CONTENTS

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Section: Discussionmentioning

confidence: 99%

Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps

et al. 2019

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“…Such systems can exhibit the spontaneous breaking of parity-time (PT ) symmetry, as well as exceptional points in parameter space, where Hamiltonian eigenvalues coalesce. A variety of phenomena in such non-Hermitian systems have been studied, including quasi-adiabatic evolution and chiral mode switching [2][3][4][5][6][7][8][9][10][11][12][13], directional invisibility [14], the possibility of enhanced parameter sensing [15][16][17][18][19], and even applications to robust wireless power transfer [20].…”

Section: Introductionmentioning

confidence: 99%

Non-Hermitian dynamics without dissipation in quantum systems

Wang

Clerk

2019

Phys. Rev. A

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Models based on non-Hermitian Hamiltonians can exhibit a range of surprising and potentially useful phenomena. Physical realizations typically involve couplings to sources of incoherent gain and loss; this is problematic in quantum settings, because of the unavoidable fluctuations associated with this dissipation. Here, we present several routes for obtaining unconditional non-Hermitian dynamics in non-dissipative quantum systems. We exploit the fact that quadratic bosonic Hamiltonians that do not conserve particle number give rise to non-Hermitian dynamical matrices. We discuss the nature of these mappings from non-Hermitian to Hermitian Hamiltonians, and explore applications to quantum sensing, entanglement dynamics and topological band theory. The systems we discuss could be realized in a variety of photonic and phononic platforms using the ubiquitous resource of parametric driving.

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“…Associated with EPs, many interesting wave phenomena have been theoretically studied and experimentally observed [6]. These unique features have found valuable applications in unidirectional propagation [7], lasing [8][9][10][11], sensing [12][13][14][15][16], mode conversion [17], and spontaneous emission processes [18]. Many works on EPs and their applications are associated with parity-time (PT ) symmetric optical systems with a balanced gain and loss [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Exceptional points for resonant states on parallel circular dielectric cylinders

Abdrabou

2019

J. Opt. Soc. Am. B

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Exceptional points (EPs) are special parameter values of a non-Hermitian eigenvalue problem where eigenfunctions corresponding to a multiple eigenvalue coalesce. In optics, EPs are associated with a number of counter-intuitive wave phenomena, and have potential applications in lasing, sensing, mode conversion and spontaneous emission processes. For open photonic structures, resonant states are complex-frequency solutions of the Maxwell's equations with outgoing radiation conditions. For open dielectric structures without material gain or loss, the eigenvalue problem for resonant states can have EPs, since it is non-Hermitian due to radiation losses. For applications in nanophotonics, it is important to understand EPs for resonant states on small finite dielectric structures consisting of conventional dielectric materials. To achieve this objective, we study EPs of resonant states on finite sets of parallel infinitely-long circular dielectric cylinders with subwavelength radii. For systems with two, three and four cylinders, we develop an efficient numerical method for computing EPs, present examples for second and third order EPs, and highlight their topological features. Our work provides insight to understanding EPs on more complicated photonic structures, and can be used as a simple platform to explore applications of EPs.

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Quantum Noise Theory of Exceptional Point Amplifying Sensors

Cited by 218 publications

References 40 publications

Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps

Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps

Non-Hermitian dynamics without dissipation in quantum systems

Exceptional points for resonant states on parallel circular dielectric cylinders

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