We show that detection of single photons is not subject to the fundamental limitations that accompany quantum linear amplification of bosonic mode amplitudes, even though a photodetector does amplify a few-photon input signal to a macroscopic output signal. Alternative limits are derived for nonlinear photon-number amplification schemes with optimistic implications for single-photon detection. Four commutator-preserving transformations are presented: one idealized (which is optimal) and three more realistic (less than optimal). Our description makes clear that nonlinear amplification takes place, in general, at a different frequency ω' than the frequency ω of the input photons. This can be exploited to suppress thermal noise and dark counts past what is possible with linear amplification up to a fundamental limit imposed by nonlinear amplification into a single bosonic mode.
We show that detection of single photons is not subject to the fundamental limitations that accompany quantum linear amplification of bosonic mode amplitudes, even though a photodetector does amplify a few-photon input signal to a macroscopic output signal. Alternative limits are derived for nonlinear photon-number amplification schemes with optimistic implications for single-photon detection. Four commutator-preserving transformations are presented: one idealized (which is optimal) and three more realistic (less than optimal). Our description makes clear that nonlinear amplification takes place, in general, at a different frequency ω' than the frequency ω of the input photons. This can be exploited to suppress thermal noise and dark counts past what is possible with linear amplification up to a fundamental limit imposed by nonlinear amplification into a single bosonic mode.
We show that detection of single photons is not subject to the fundamental limitations that accompany quantum linear amplification of bosonic mode amplitudes, even though a photodetector does amplify a few-photon input signal to a macroscopic output signal. Alternative limits are derived for nonlinear photon-number amplification with optimistic implications for single-photon detection. Our description makes clear that nonlinear amplification takes place, in general, at a different frequency ω′ than the frequency ω of the input photons, which can be exploited to suppress thermal noise even further. A practical example that fits our description very well is electron shelving.
Quantum mechanics cements the intimate relationship between the nature of light and its detection. Historically, quantum theories of photodetection have generally fallen into two categories: the first tries to determine what quantum field observable is measured when photoelectrons are detected, laying the theoretical groundwork for photodetection being possible. The second type are phenomenological theories, which take great care to model the details of specific photodetectors. In this dissertation, we fill in the gap between these two models in the modern literature on photodetection by constructing a fully quantum-mechanical and sufficiently realistic model that includes all stages of the photodetection process. We accomplish this within the framework of quantum information theory using the language of positive operator valued measures (POVMs). \n\nA POVM provides the most general description of a quantum measurement. In the context of single-photon detection, the photodetector POVM provides a complete characterization of the single-photon detector (SPD) from which all figures of merit can be calculated. Each element of the POVM is comprised of a weighted sum over single-photon state projectors. To construct SPD POVMs, we identify the states projected onto by a measurement and the associated weights. We first accomplish this for a simple time-dependent system, laying out how to efficiently project onto arbitrary single-photon states. Then, we describe the three stages of a realistic SPD: transmission, amplification, and measurement.\n\nIn the transmission stage of photodetection a photon enters a network of discrete energy levels, its energy propagating through that network and finally exiting into another output continuum of modes, a process entirely described by a single complex function. In the amplification stage of photodetection, a single excitation is amplified into a macroscopic signal via a nonlinear amplification mechanism. In the final stage, an inefficient ``classical'' measurement is made on the macroscopic signal. By combining these three stages we form a chain of inference from the final ``click'' to the input photon and construct a POVM projecting onto the input Hilbert space. Lastly, we discuss limits and tradeoffs that arise at each stage and implications for photodetection applications.\n\nThis dissertation contains previously published and unpublished material.
Does quantum mechanics allow for deterministic amplification schemes that simultaneously behave uniformly for all angles of bosonic phase space (i.e. phase preserving) and are nonlinear in the underlying field operators? Would such a scheme have some utility to quantum information science? In this paper we answer both questions with a resounding yes. Such amplifiers exist, but their form is highly constrained compared to the more general set of noise limited nonlinear amplifiers previously studied in the literature. This enables us to characterize the entire class of bosonic noise-limited nonlinear phase preserving amplifiers, and identify their utility: namely, the optimal amplification of Yurke-Stoler cat states and Kerr kitten states.
Linear quantum amplifiers are indispensable tools for quantum technologies, yet their performance is fundamentally limited by quantum noise, precluding any signal-to-noise ratio (SNR) enhancement unless supplemented by post-selection or non-classical resources. To surpass this limitation, we propose a nonlinear quantum amplification strategy that exploits the interplay between a gain-stabilized bright eigenmode of a coupled two-mode bosonic system and Kerr nonlinearity. We demonstrate that this interplay enables the signal gain to surpass the noise gain in a selected quadrature, leading to a net increase in the SNR beyond the quantum limits of conventional linear amplifiers. Our work thus establishes a novel nonlinear amplification paradigm capable of enhancing the SNR, with promising applications across quantum information processing, quantum communications, and quantum metrology.
Quantum mechanics cements the intimate relationship between the nature of light and its detection. Historically, quantum theories of photodetection have generally fallen into two categories: the first tries to determine what quantum field observable is measured when photoelectrons are detected, laying the theoretical groundwork for photodetection being possible. The second type are phenomenological theories, which take great care to model the details of specific photodetectors. In this dissertation, we fill in the gap between these two models in the modern literature on photodetection by constructing a fully quantum mechanical and sufficiently realistic model that includes all stages of the photodetection process: transmission, amplification, and a final classical measurement. We accomplish this within the framework of quantum information theory using the language of positive operator valued measures (POVMs). This dissertation contains material previously published in three papers: Propp, Tz. B & van Enk, S. J. (2019). On nonlinear amplification: improved quantum limits for photon counting. Optics Express 27, 16, 23454-23463. Propp, Tz. B & van Enk, S. J. (2019). Quantum networks for single photon detection. Physical Review A, 100, 033836. Propp, Tz. B & van Enk, S. J. (2020). How to project onto an arbitrary single-photon wavepacket. Physical Review A, 102, 053707.
Quantum amplifiers are intrinsically nonlinear systems whose performance limits are set by quantum mechanics. In quantum measurement, amplifier operation is conventionally optimized in the linear regime by maximizing signal-to-noise ratio, an objective that is well-suited to parameter estimation but is typically insufficient for more general tasks such as arbitrary quantum state discrimination. Here we show that single-shot quantum state classification can benefit from operating a quantum amplifier outside the linear regime, when the measurement chain is optimized end-to-end for a task-specific cost function. We analyze a realistic superconducting readout architecture that includes state preparation, cryogenic nonlinear amplification, and room-temperature detection with finite noise. By introducing performance metrics tailored to state discrimination, we identify operating regimes in which nonlinear amplification provides a measurable advantage and clarify the trade-offs that ultimately limit classification fidelity. Building on these results, we propose a qubit readout architecture without cavity displacement that exploits nonlinear amplification to enhance single-shot state discrimination performance. Our results establish the practical value of nonlinear quantum amplifiers for quantum state discrimination and lay the foundation for a broader program to develop a general, end-to-end framework for resource-constrained optimization of nonlinear amplification in quantum information processing tasks.