Enhanced Whispering Gallery Mode Phase Shift using Indistinguishable Photon Pairs

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: We're looking at the paper: "Enhanced Whispering Gallery Mode Phase Shift using Indistinguishable Photon Pairs".

Mira: Here's the gist of the paper. The gist: The paper presents a theoretical investigation showing that an input state of an indistinguishable photon pair leads to a bimodal coincidence transmission spectrum when coupled to a whispering gallery mode resonator, resulting in at least a four-fold improvement in the signal-to-noise ratio (SNR) for WGM sensing Quantum Optical Model for WGM Coupling The model uses the operator valued phasor addition (OVPA) approach described in Ref.

12: for a quantum optical treatment of coupling an optical mode in a waveguide to a ring resonator.

Mira: The coupling to the resonator is characterized by the amplitude coupling coefficient κ and amplitude reflection coefficient r, where κ2 + r2 = 1.

Kai: The mode in the ring resonator has an amplitude transmission α and phase θ per round trip.

Title and authors: Kai: So let's talk about who wrote this—callum jones, antonio vidiella-barranco, jolly xavier, and frank vollmer. They’re bringing together the hardware side and the theory here.

Mira: I think it’s interesting because they are taking a fairly complex setup involving WGM resonators and coupling them to a Mach-Zehnder interferometer, which is the context for this kind of sensing.

Lev: From my side, I’m looking at how this relates to what we can actually build. It involves these coupling coefficients κ and r where κ squared plus r squared equals one, so that’s the basic physics of coupling you have to manage in real hardware.

Kai: Exactly, Lev. It shows the math behind what you have to engineer in your setup when you are trying to get a good signal out of it.

Mira: And they are using a specific model for this, the operator valued phasor addition approach from reference twelve which is how they treat the quantum optical part of coupling a mode into a resonator <ref:2404.17409#pg2>.

The paper's summary: Kai: Now let's get into what the paper actually says in its summary. It talks about taking that input state and seeing how it plays out inside the interferometer after coupling to the WGM.

Mira: Basically, they describe this two-photon N00N state that appears due to Hong-Ou-Mandel interference at the first beamsplitter when you feed in those indistinguishable photons.

Lev: That N00N state is key because it introduces a double phase shift, which means the phase difference between the two photons in modes five and six is twice what you would normally expect from just coupling to a WGM resonator.

Kai: So that doubled phase shift is what makes their results interesting; it changes how the final output state looks when you act on those modes with an output beamsplitter.

Mira: They show the final output state equation, which involves terms depending on A over t squared, and specifically highlights where that double phase shift comes into play in the modes five and six.

The paper's improvements: Kai: The main improvement they highlight is comparing three measurement cases: 'Classical WGM', 'Classical WGM-MZI', and then the 'Entangled WGM-MZI' case.

Mira: For the entangled case, they give us a coincidence probability formula that looks like PCoinc(ω) equals one over four A over t squared plus one.

Lev: What we see is that in the overcoupled regime, where alpha equals zero point nine nine nine seven and r equals zero point nine nine nine six, the entangled WGM-MZI has reduced noise in the wavelength shift compared to those two classical cases you mentioned earlier <ref:2404.17409#pg1>.

Kai: And they say that for this overcoupling region, the SNR enhancement factor for the entangled WGM-MZI relative to a classical WGM is consistently higher and it peaks at that critical coupling condition.

Mira: They also look at the uncertainty delta omega, which shows that for photon number N greater than one hundred five the resonance frequency noise dominates and stays constant even as the optical power increases.

Conclusion: Kai: So to wrap up this paper, they show that using an indistinguishable photon pair input state can lead to a four-fold improvement in SNR for WGM sensing.

Mira: And they found that this advantage is most robust in the overcoupled regime, especially when considering the spectral width of the input photons.

Lev: From a hardware standpoint, they suggest that the optimum enhancement is a trade-off between having noise much lower than your dynamic range and having a more overcoupled resonator.

Kai: It points toward needing to tune those parameters carefully based on what you want to measure, whether it’s temperature or pressure sensing.

Mira: This work suggests that using these quantum input states can really help improve the performance of WGM sensors in applications like biosensing or single molecule detection.

Lev: And they point out a limitation, though, that the most robust SNR advantage is obtained when you are in the overcoupling regime, which might not always be achievable depending on your experimental constraints.

Kai: So yeah, this paper shows a path forward for getting better sensitivity in these specific quantum sensing applications.