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arXiv:2404.17409

Enhanced Whispering Gallery Mode Phase Shift using Indistinguishable Photon Pairs

Callum Jones, A. Vidiella-Barranco, Jolly Xavier, Frank Vollmer

Published Apr 26, 2024• 1 citation
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Abstract

We present a theoretical investigation of a whispering gallery mode (WGM) resonator coupled to a Mach-Zehnder interferometer (MZI) and show a bimodal coincidence transmission spectrum when the input state is an indistinguishable photon pair. This is due to the doubled WGM phase shift experienced by the path-entangled state in the interferometer. Further, we model the noise in a WGM resonance shift measurement comparing photon pairs with a coherent state. At least a four-fold improvement in the signal-to-noise ratio (SNR) is possible, with clear implications for quantum-enhanced WGM sensing.

DOI
10.48550/arxiv.2404.17409

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We present a theoretical investigation of a whispering gallery mode (WGM) resonator coupled to a Mach-Zehnder interferometer (MZI) and show a bimodal coincidence transmission spectrum when the input state is an indistinguishable photon pair. This is due to the doubled WGM phase shift experienced by the path-entangled state in the interferometer. Further, we model the noise in a WGM resonance shift measurement comparing photon pairs with a coherent state. At least a four-fold improvement in the signal-to-noise ratio (SNR) is possible, with clear implications for quantum-enhanced WGM sensing.
We study the estimation of detuning and intrinsic loss in a lossy whispering-gallery-mode (WGM) resonator located in a balanced Mach--Zehnder interferometer. We use indistinguishable photon pairs and coherent-state probes. We show that using indistinguishable photon pairs can provide higher Quantum Fisher Information (QFI) of dissipative parameters, such as intrinsic loss, at resonance away from critical coupling. Taking into account all photon-loss outcomes, we obtain analytical QFI expressions and compare photon-pair and coherent-state probe results when they have the same mean photon number. For estimating the round-trip amplitude transmission at resonance and away from critical coupling, the photon-pair probe gives a higher QFI than the coherent-state probe, and photon-number-resolved detection saturates this QFI. This advantage is due to the photon-loss statistics and it is still accessible for a typical overcoupled condition after averaging over fluctuations of the unresolved detuning. We identify the limits of this advantage: phase doubling does not improve resonant detuning estimation, and coincidence-only detection is inefficient close to a zero transmission. These results identify the cases in which photon pairs can be useful for absorption and pump--probe WGM sensing.
Phase-shifting interferometry (PSI) promises excellent performance for quantitative phase measurement. However, the PSI is commonly realized by utilizing the Mach-Zehnder interferometer (MZI) fed with classical resources, and hence its phase sensitivity is hindered by the photon shot noise. In this paper, we propose to introduce specific phase-shifting algorithms into the well-established quantum-enhanced MZI, seeded by coherent and squeezed vacuum states and followed by single-mode intensity detection and difference intensity detection, to achieve quantitative phase measurement with sensitivity beyond that achieved by the corresponding Mach-Zehnder-type PSI with classical input. We show that when the average photon number of the coherent state is dominant, the optimal phase sensitivity of the Mach-Zehnder-type PSI with coherent plus squeezed vacuum input is better than the phase sensitivity of the Mach-Zehnder-type PSI with single coherent input under the same phase-sensing intensity condition in both of detection setups. We also show that for the typical MZI seeded with a high-power coherent state and a finitely squeezed vacuum state, the combination of intensity detection and phase-shifting algorithm can still improve the sensitivity of quantitative phase measurement. Furthermore, we derive the phase sensitivity of the fixed MZI as well as the quantum Cramér-Rao bound for two detection schemes. Finally, we explore the impacts of photon losses on the phase sensitivity enhancements of the Mach-Zehnder-type PSI and the fixed MZI in the high-intensity regime for each detection setup. The robustness to losses is compared between the Mach-Zehnder-type PSI and the fixed MZI. Our results may be helpful to promote the exploration of quantum-enhanced quantitative phase sensing.
Whispering Gallery Mode Resonators (WGMRs) made ofχ2\chi^{2}χ2nonlinear dielectric materials have been shown to be a versatile source of quantum states [1]–[4]. Here, we investigate this type of source and demonstrate a Hong-Ou-Mandel (HOM) interference between heralded photon pairs that are produced in two spontaneous parametric downconversion (SPDC) processes within a single WGMR [5]. The WGMR is pumped by a continuous-wave laser with only 100 nW in total from the clockwise (CW) and counterclockwise (CCW) directions in two degen-erate counter-propagating modes. Hence, the heralded photon pairs from the two directions are indistinguishable in frequency. The indistinguishability of spatial and polarization modes is achieved by using standard optical elements. We measure the Glauber correlation function,gsi(2)(t)g_{si}^{(2)}(t)gsi(2)​(t), from both directions, and find that the two functions are almost identical. As a result, the photon pairs generated from both directions are highly indistinguishable in the temporal domain (See Fig. 1(a)). The signal photons emitted in both directions are combined on a beam splitter, while the idler photons are coupled directly into detectors. The HOM interference fringe is extracted by detecting four-fold coincidence counts. The highest measured HOM visibilities reach a value above 74% (See Fig. 1(b)). We also show that the visibilities change when the value ofgsi(2)(0)g_{si}^{(2)}(0)gsi(2)​(0)varies, and it agrees well with the theoretical prediction provided by Ref. [6]. (See Fig. 1(c)). Finally, we measure the Glauber correlation function from two different WGMRs (See Fig. 1(d)) showing that the two functions are almost identical. This indicates that it is possible to match the temporal mode of heralded photon pairs from different WGMRs. Together with the extremely low pump power requirement, WGMRs could be a potential platform for large-scale quantum applications.
Abstract Crystalline whispering gallery mode resonators (WGMRs) have been shown to facilitate versatile sources of quantum states that can efficiently interact with atomic systems. These features make WGMRs an efficient platform for quantum information processing. Here, we experimentally show that it is possible to generate polarization entanglement from WGMRs by using an interferometric scheme. Our scheme gives us the flexibility to control the phase of the generated entangled state by changing the relative phase of the interferometer. The S value of Clauser–Horne–Shimony–Holt’s inequality in the system is 2.45 ± 0.07, which violates the inequality by more than six standard deviations.
We report a novel, to the best of our knowledge, way to achieve phase-controlled dual-wavelength resonance based on whispering-gallery-mode (WGM) microcavities experimentally. With the help of a feedback waveguide, not only two optical pathways but also a unidirectional coupling between counter-propagating waves are formed, which is the requirement of all-optical analogues of electromagnetically induced transparency and Autler-Townes splitting. By adjusting the accumulating phase introduced from the fiber waveguide, we observe the signal lineshape changes from symmetric to asymmetric, i.e., the resonant transmission and extinction ratio of two splitting modes can be controlled, which brings a new degree of freedom to the WGM resonator system. These results may boost the development of quantum state control and pave the way for reconfiguring devices such as narrow-band filters.
A nonlinear phase shift is introduced to a Mach-Zehnder interferometer (MZI), and we present a scheme for enhancing the phase sensitivity. In our scheme, one input port of a standard MZI is injected with a coherent state and the other input port is injected with one mode of a two-mode squeezed-vacuum state. The final interference output of the MZI is detected with the method of active correlation output readout. Based on the optimal splitting ratio of beam splitters, the phase sensitivity can beat the standard quantum limit and approach the quantum Cram\'er-Rao bound. The effects of photon loss on phase sensitivity are discussed. Our scheme can also provide some estimates for units of ${\ensuremath{\chi}}^{(3)}$, due to the relation between the nonlinear phase shift and the susceptibility ${\ensuremath{\chi}}^{(3)}$ of the Kerr medium.