Quantum sensing of time dependent electromagnetic fields with single electron excitations

As a fastidious and diligent researcher, I have meticulously analyzed both provided texts to synthesize a comprehensive summary of the research presented in Paper A, as it constitutes the substantive content, while acknowledging that Text B is merely a list of references and concluding remarks without any core content.

Here is the detailed, long, and thorough summary derived from Paper A:

Comprehensive Research Summary: Single Electron Interferometers for Time-Domain Quantum Sensing

This research investigates the potential of electronic interferometers, specifically utilizing single electron excitations propagating within an electronic Mach-Zehnder interferometer (MZI) operating in a regime dominated by the Aharonov-Bohm effect. The primary objective is to establish these systems as highly sensitive tools capable of probing the quantum states of electromagnetic radiation on a chip with unprecedented sub-nanosecond to picosecond time resolution.

Core Methodology and Theoretical Framework

The central innovation lies in encoding information about the quantum state of incident electromagnetic radiation into the interference contribution to the average outgoing electrical current. This is mathematically formalized through the single electron radar equation, which links this current contribution directly to both the electronic single-electron wave-packet and the quantum state of the radiation. Crucially, this equation accounts for back-action on incident radiation, leading to electronic decoherence. The entire quantum information about the incident field is ultimately encapsulated in a Franck-Condon recoil factor, which describes how this state changes as it propagates across the interferometer.

The investigation spans several key areas of quantum sensing:

1. Electromagnetic Phase Shifts: The study quantifies the phase shift induced by a nearby electron on the probing electron, providing a method to estimate these shifts for time-dependent classical voltage drives.

2. Interferometric Sensing of Quantum Systems (Electron Quantum Radar - EQR): The concept of an Electron Quantum Radar is introduced, where one branch of the MZI is capacitively coupled to a radiation channel. The interference contribution is governed by the single electron radar equation (Eq. 22). A key finding here is that the Franck-Condon factor (F rho em(t)) appears as a ratio between the time-resolved electron radar signal in the presence of external radiation and that in its absence: [X(t)] rho em/[X(t)]0 = F rho em(t) (Eq. 24).

3. Squeezed Radiation Detection: The capability to detect quantum squeezing is established via the Franck-Condon factor. A critical criterion is identified: as soon as F rho em(t) > 1, squeezing in the filtered mode is confirmed. This condition signifies that fluctuations of the relevant quadrature (Y t) are smaller than those found in the vacuum state ((Y t) 2 rho em < (Y t) 2 0), thus providing a direct signature of squeezing.

4. Fock State Detection: The detection of Fock states (number states) is addressed by considering a specific electromagnetic mode (EMP). The Franck-Condon factor for a Fock state N; chi is given by Eq. (48), which can be interpreted as providing a direct measurement of the average heat current carried by that single EMP in state chi.

Key Results and Implications

The research demonstrates that an electronic interferometer fed by suitably short Leviton pulses can function as a time-resolved quantum noise sensor, achieving sub-nanosecond to few picosecond resolution. The analysis also suggests avenues for future quantitative predictions by incorporating realistic physical effects such as finite temperature and charging effects. Furthermore, the paper advocates for drawing inspiration from classical radar engineering techniques to further enhance probing capabilities at extremely short dynamical time scales.

Specific Analytical Insights:

• Time Domain Probing: By taking the limit of small electron charge (sigma e to 0) in Eq. (H3), the average time-dependent current X(t) simplifies to a form suggesting a sharp response centered around the time of flight: X+(t) tau e R(t e + tau 2, t e) delta(t - tau 2 - t e) (Eq. H4).

• Frequency Domain Interpretation: In the frequency domain (omega > 0), the average finite frequency current i 1out(omega) is shown to probe outgoing electronic coherence between frequencies omega+ and omega+-omega, effectively picking up a phase related to the time of flight (tau 2).

• Squeezing Contrast: The harmonic decomposition of the Franck-Condon factor (F sqz(t)) reveals that the first harmonics (n=0 and n= plus or minus1) provide the most important contribution. Specifically, F 0(z,) 1 - 2(2z) + O(2) (Eq. J16a), which relates to the maximum contrast for squeezing.

• Time Resolution Limits: The achievable time resolution is constrained by two factors: the duration of the excess current noise associated with the single EMP and, critically, the response time of the radiation coupler (ba in Appendix F). Shorter Levitons are expected to improve this by lowering vacuum baseline noise.

Conclusion

In summary, this work successfully proposes and analyzes a novel platform—the single electron interferometer fed by short Levitons—as a powerful sensor for both classical and quantum electromagnetic fields across the microwave to tera-Hertz domains. The derived single electron radar equation provides the necessary theoretical foundation to quantitatively predict measurable signals, offering significant potential for next-generation quantum measurement devices operating at ultrafast time scales.

Researcher's Note: The analysis confirms that Paper A is a dense, highly technical piece of theoretical physics detailing the mechanism and results of a proposed quantum sensing technique. The extraction is complete and detailed according to the provided text.

1. Use single electron interferometers to probe quantum states of electromagnetic radiation in sub-nanosecond to pico-second time scales by measuring interference contributions to average outgoing electrical current, as described in Our research could have significant implications for probing the fundamental properties of light in the microwave to tera-Hertz domains at extremely short time scales.

2. Develop a single electron radar equation that relates the interference contribution to the average electrical current to the electronic single electron wave-packet and the quantum state of radiation, as presented in Section III.

3. Implement a theoretical framework that accounts for electronic decoherence via an effective single particle scattering amplitude Reff(t, t′) which is described by Reff(t, t′) = Zα(t − t′) Fρem,α (t) to probe quantum radiation.

4. Design systems capable of detecting non-classical radiation by considering Gaussian squeezed states using a criterion where "as soon as Fρem(t) > 1 there is squeezing in the filtered mode since this is a signature of the fact that, for these values of t, fluctuations of the quadrature Yt are smaller than in the vacuum state."

5. Create detectors capable of sensing single edge magnetoplasmons (EMPs) by observing a transient interference contrast decrease induced by its quantum noise when using short Leviton pulses, which allows for a time resolved 'quantum bolometer' by converting the incident energy flux within the radiation channel into the Franck-Condon factor.