Abstract

Exceptional points are spectral singularities in open quantum and wave systems that exhibit a strong spectral response to perturbations. This feature can be exploited for a new generation of sensors. This paper explains the basic mechanism and comprehensively reviews the recent developments. In particular, it highlights the influence of classical noise and fundamental limitations due to quantum noise.

© 2020 Chinese Laser Press

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2020 (5)

C. Wang, X. Jiang, G. Zhao, M. Zhang, C. W. Hsu, B. Peng, A. D. Stone, and L. Yang, “Electromagnetically induced transparency at a chiral exceptional point,” Nat. Phys. 16, 334–340 (2020).
[Crossref]

A. Jian, F. Liu, G. Bai, B. Zhang, Y. Zhang, Q. Zhang, X. Xue, S. Sang, and X. Zhang, “Parity-time symmetry based on resonant optical tunneling effect for biosensing,” Opt. Commun. 475, 125815 (2020).
[Crossref]

J.-H. Park, A. Ndao, L. Hsu, A. Kodigala, T. Lepetit, Y.-H. Lo, and B. Kanté, “Symmetry-breaking-induced plasmonic exceptional points and nanoscale sensing,” Nat. Phys. 16, 462–468 (2020).
[Crossref]

J. Wiersig, “Robustness of exceptional-point-based sensors against parametric noise: the role of Hamiltonian and Liouvillian degeneracies,” Phys. Rev. A 101, 053846 (2020).
[Crossref]

H. Wang, Y.-H. Lai, Z. Yuan, M.-G. Suh, and K. Vahala, “Petermann-factor sensitivity limit near an exceptional point in a Brillouin ring laser gyroscope,” Nat. Commun. 11, 1610 (2020).
[Crossref]

2019 (18)

F. Minganti, A. Miranowicz, R. W. Chhajlany, and F. Nori, “Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: the effects of quantum jumps,” Phys. Rev. A 100, 062131 (2019).
[Crossref]

M. Zhang, W. Sweeney, C. W. Hsu, L. Yang, A. D. Stone, and L. Jiang, “Quantum noise theory of exceptional point amplifying sensors,” Phys. Rev. Lett. 123, 180501 (2019).
[Crossref]

C. Chen, L. Jin, and R.-B. Liu, “Sensitivity of parameter estimation near the exceptional point of a non-Hermitian system,” New J. Phys. 21, 083002 (2019).
[Crossref]

C. Wolff, C. Tserkezis, and N. A. Mortensen, “On the time evolution at a fluctuating exceptional point,” Nanophotonics 8, 1319–1326 (2019).
[Crossref]

Z. Xiao, H. Li, T. Kottos, and A. Alù, “Enhanced sensing and nondegraded thermal noise performance based on PT-symmetric electronic circuits with a sixth-order exceptional point,” Phys. Rev. Lett. 123, 213901 (2019).
[Crossref]

Z. Dong, Z. Li, F. Yang, C.-W. Qiu, and J. S. Ho, “Sensitive readout of implantable microsensors using a wireless system locked to an exceptional point,” Nat. Electron. 2, 335–342 (2019).
[Crossref]

C. Zeng, Y. Sun, G. Li, Y. Li, H. Jiang, Y. Yang, and H. Chen, “Enhanced sensitivity at high-order exceptional points in a passive wireless sensing system,” Opt. Express 27, 27562–27572 (2019).
[Crossref]

M. P. Hokmabadi, A. Schumer, D. N. Christodoulides, and M. Khajavikhan, “Non-Hermitian ring laser gyroscopes with enhanced Sagnac sensitivity,” Nature 576, 70–74 (2019).
[Crossref]

Y.-H. Lai, Y.-K. Lu, M.-G. Suh, Z. Yuan, and K. Vahala, “Observation of the exceptional-point-enhanced Sagnac effect,” Nature 576, 65–69 (2019).
[Crossref]

M. Naghiloo, M. Abbasi, Y. N. Joglekar, and K. W. Murch, “Quantum state tomography across the exceptional point in a single dissipative qubit,” Nat. Phys. 15, 1232–1236 (2019).
[Crossref]

Q. Zhong, J. Ren, M. Khajavikhan, D. N. Christodoulides, Ş. K. Özdemir, and R. El-Ganainy, “Sensing with exceptional surfaces in order to combine sensitivity with robustness,” Phys. Rev. Lett. 122, 153902 (2019).
[Crossref]

Q. Zhong, S. Nelson, Ş. K. Özdemir, and R. El-Ganainy, “Controlling direction absorption with chiral exceptional surfaces,” Opt. Lett. 44, 5242–5245 (2019).
[Crossref]

S. Wang, B. Hou, W. Lu, Y. Chen, Z. Q. Zhang, and C. T. Chan, “Arbitrary order exceptional point induced by photonic spin-orbit interaction in coupled resonators,” Nat. Commun. 10, 832 (2019).
[Crossref]

J. Kullig and J. Wiersig, “High-order exceptional points of counterpropagating waves in weakly deformed microdisk cavities,” Phys. Rev. A 100, 043837 (2019).
[Crossref]

J. Wiersig, “Nonorthogonality constraints in open quantum and wave systems,” Phys. Rev. Res. 1, 033182 (2019).
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Figures (5)

Fig. 1.
Fig. 1. Illustration of the enhanced frequency splitting induced by perturbing a non-Hermitian Hamiltonian at an exceptional point of second order (red curve) compared to the case of a conventional degeneracy (blue dash-dotted curve). In both cases, the same perturbation has been applied. (a) Splitting versus perturbation strength ε. (b) Spectra for fixed ε designated by the vertical line in (a). The double-arrowed lines indicate the splitting, which is considerably larger for the exceptional point.
Fig. 2.
Fig. 2. Two proposals for EP-based sensors. (a) Microdisk cavity with two external scatterers (particles or nano-tips on the right) which implement an EP2 by generating fully asymmetric backscattering. As a result, only one mode [here counterclockwise (CCW) propagating] of the given mode pair exists. A target particle shown on the left induces additional backscattering, leading to an enhanced frequency splitting. (b) PT-symmetric pair of microrings, one with gain (ring 1) and one with loss (ring 2).
Fig. 3.
Fig. 3. Various experimental realizations of EP-based sensors. (a) Optical image of a microtoroidal cavity together with a fiber-taper waveguide and three nano-tips for particle detection. Reprinted by permission from Springer Nature: Nature [73], copyright 2017. (b) Illustration and SEM (scanning electron microscope) image of a PT-symmetric ternary microring system for thermal sensing; inset exposes the heating elements underneath each cavity for fine-tuning and thermal perturbation. Reprinted by permission from Springer Nature: Nature [74], copyright 2017. (c) Sketch of a ring laser gyroscope with three mirrors, a Faraday rotator (FR), a half-wave plate (HWP), two Brewster windows (BW), and a He–Ne gas tube as gain medium. Reprinted by permission from Springer Nature: Nature [80], copyright 2019. (d) Computed tomography reconstruction of a wireless PT-symmetric microsensor implanted in a rat abdomen. Reprinted by permission from Springer Nature: Nature Electronics [78], copyright 2019. (e) Schematics and optical image of the thermo-sensitive microscope slide for thermal mapping; from Ref. [75]. (f) Illustration of a laser gyroscope with stimulated Brillouin laser (SBL) action pumped optically at two different frequencies ωp1 and ωp2 via an attached waveguide which induces backscattering with rate κ. Reprinted by permission from Springer Nature: Nature [81], copyright 2019.
Fig. 4.
Fig. 4. Results on the microtoroidal sensor in the experiment of Chen et al. [73]. The transmission spectra of a DP-based sensor (a) before and (b) after adsorption of a target particle on the surface of the cavity. The transmission spectra of an EP-based sensor (c) before and after (d) adsorption of the same target particle. The blue arrows illustrate the symmetric backscattering at the target particle, and the red arrow marks the fully asymmetric backscattering related to the EP. The dashed vertical lines in (b) and (d) pinpoint the resulting frequency splitting. (e) Measured splitting enhancement factor versus perturbation strength ε. The double logarithmic plot in the inset displays the two different splittings versus ε. The DP-based sensor (red circles) exhibits a slope of 1, whereas the EP-based sensor (blue squares) exhibits a slope of 1/2 (solid black line) for sufficiently small perturbations, confirming the square-root behavior at an EP2. Reprinted by permission from Springer Nature: Nature [73], copyright 2017.
Fig. 5.
Fig. 5. Fundamental limit of an EP-based laser gyroscope due to excess quantum noise [94]. (a) Measured stimulated Brillouin laser (SBL) beating frequency versus pump detuning (which determines the frequency detuning of the uncoupled SBL modes) for different locking zones. The inset shows an Allan deviation measurement of frequency σν versus gate time τ. (b) Measured white frequency noise of the beating signal determined using the Allan deviation measurement. The linewidth enhancement factor [Petermann factor (PF), solid curves] and the noise enhancement factor (NEF, dashed curves) are theoretical predictions. The figure is taken from Ref. [94].

Equations (24)

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iddt|ψ=H^|ψ.
H^(ε)=H^0+εH^1,
H^0|DP=(E000E0),
H^0|EP=(E0A00E0)
H^1=(E1A1B1E2),
ΔEDP=ε(E2E1)2+4A1B1.
ΔEEP=εε(E2E1)2+4A0B1+4εA1B1=ε4A0B1+O(ε),
|A0|2|ImE0|.
H^0|EP=(E0100E0100E0).
H^0=(ω0+iαggω0iα).
E±=ω0±g2α2.
H^1=(1000).
H^0=(iακ0κ0κ0κiα).
H^1=(100000000).
H^0=(ω0+iαg0gω0iα000ωsiγs),H^1=(001001110).
H^0=(ω0iγ1ggω0iγ2)
H^1=(1001)
H^0=(ω1iγiκiκω2iγ)
H^tot(t)=H^(ε)+j=1Kξj(t)H^noise,j,
H^noise,1=(1001).
dρ^dt=Lρ^+P^(ω)
Lρ^=i(H^effρ^ρ^H^eff)+jγjH^noise,jρ^H^noise,j,
H^eff(ε)=H^(ε)i2jγjH^noise,j2.
iddt(a^1a^n)=H^(ε)(a^1a^n)+driving+bath coupling.

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