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The birth, life, and death of squeezed light

Christian Drago

Published Jun 1, 2026• 0 citations
OpenAlex

Abstract

In this thesis we study three aspects of squeezed light. First, we investigate the generation of pulsed, near‑pure, degenerate, single‑temporal‑mode squeezed light produced by dual‑pump spontaneous four wave mixing in integrated silicon‑nitride coupled‑ring resonators. We show that parasitic spontaneous four wave mixing processes inherent to the dual‑pump configuration can substantially degrade the amount of generated squeezing and state purity. To mitigate these effects we explore pump detuning, engineered dispersion, and an auxiliary‑ring structure as suppression strategies. We then optimize the incident pump amplitude and phase, demonstrating that longer pump pulses can yield highly squeezed, temporally separable states and that an appropriate pre‑chirp tracks the effects of self‑ and cross‑phase modulation, increasing intracavity pump amplitudes and the amount of generated squeezing. Next, we analyze the spectral–temporal structure and photon statistics of strongly correlated squeezed light. We develop a general formalism based on the Whittaker–Shannon interpolation of the joint‑temporal amplitude that is particularly useful in the long‑pulse and continuous‑wave limits, where the instantaneous photon density is low but the total photon number may be large. This packet‑based description provides a local, physically transparent account of the state and its photon statistics that complements the Schmidt decomposition, and extends to nonclassical states for which a Schmidt decomposition is not available. Finally, we examine whether or not squeezed illumination can enhance two‑photon excitation relative to classical light, and whether any enhancement is experimentally detectable. We construct a model including radiative and nonradiative broadening to compute scattered and absorbed energy, and apply it to fluorescence from cesium atoms in a magneto‑optical trap driven by classical and squeezed light in both continuous‑wave and pulsed regimes. Under ideal conditions squeezed light can produce a measurable enhancement in both limits, but the gains are moderate and smaller than some recent molecular reports; additional broadening or loss would further reduce detectability.

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Deconstructing squeezed light: Schmidt decomposition versus the Whittaker-Shannon interpolation

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We develop a formalism to describe squeezed light with large spectral-temporal correlations. This description is valid in all regimes, but is especially applicable in the long pulse to continuous-wave limit where the photon density at any particular time is small, although the total number of photons can be quite large. Our method relies on the Whittaker-Shannon interpolation formula applied to the joint temporal amplitude of squeezed light, which allows us to ``deconstruct'' the squeezed state. This provides a local description of the state and its photon statistics, making the underlying physics more transparent than does the use of the Schmidt decomposition. The formalism can easily be extended to more exotic nonclassical states where a Schmidt decomposition is not possible.

Physical Review A•Aug 6, 2024•6 citations

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We develop a formalism to describe squeezed light with large spectral-temporal correlations. This description is valid in all regimes, but is especially applicable in the long pulse to continuous-wave limit where the photon density at any particular time is small, although the total number of photons can be quite large. Our method relies on the Whittaker-Shannon interpolation formula applied to the joint temporal amplitude of squeezed light, which allows us to "take apart" the squeezed state. This provides a local description of the state and its photon statistics, making the underlying physics more transparent than does the use of the Schmidt decomposition. The formalism can easily be extended to more exotic nonclassical states where a Schmidt decomposition is not possible.

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Pulsed squeezed light: characterization and applications

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Squeezed light is expected to enable new quantum metrology and quantum computation applications, but the very high degree of experimental control required in practice places severe demands on the physical devices used to generate it. As ultrafast squeezed light sources are reaching an unprecedented degree of brightness and modal control, there is a strong interest in developing methods for their experimental characterization and theoretical understanding. In this thesis, we demonstrate both a new application and a new characterization technique for pulsed squeezed light. In the first part of the thesis, we present a new metrological application of pulsed squeezed light: quantum-enhanced label-free nonlinear microscopy. Stimulated emission microscopy (SEM) is a state-of-the-art pump-probe microscopy technique whose sensitivity is ultimately limited by shot noise in the probe beam. We propose to overcome this fundamental limitation by using a sub-Poissonian probe generated via optical parametric amplification. We demonstrate an intensity-squeezed sub-picosecond pulsed probe, and a simple stimulated emission microscope. Using this squeezed probe, sub-Poissonian statistics are observed in the SEM signal. After this proof-of-principle experiment, we aim to provide an improved design for a source of intensity-squeezed light. First, we develop a theoretical framework to simulate the photon statistics of a general sub-Poissonian source, considering pulsed and focused pump and seed fields in a unified spatio-temporal description. Next, we use this framework to suggest possible improvements to our previous squeezed probe. In the second part of this thesis, we provide new theoretical and experimental tools to analyze the high gain regime of pulsed spontaneous parametric down-conversion (SPDC). We study a waveguided source capable of generating twin-beams with tens of photons in a single spatio-temporal mode. We develop a framework to efficiently simulate SPDC for an arbitrary nonlinear gain, including the effect of parasitic nonlinearities such as self-phase modulation (SPM) of the pump and cross-phase modulation (XPM) between pump and twin-beams. We experimentally characterize our source using a new technique based on stimulated difference-frequency generation (DFG). In a type-II down-conversion process, we measure the frequency generation produced not only in the orthogonal polarization to the seeding beam, but also in its same polarization, which we interpret as cascaded difference-frequency generation. We argue that the additional information obtained in this measurement allows for a self-referenced estimation of the squeezing gain. Using these measurements, we accurately fit our theoretical model, revealing that, in the high gain regime, parasitic nonlinearities strongly affect the spectral structure of the twin-beams. We propose a simple strategy to reduce the impact of these nonlinearities on the modal structure of SPDC.

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Quantum theory of nondegenerate multiwave mixing III Application to single-beam squeezed-state generation

Seng‐Tiong Ho, Prem Kumar, Jeffrey H. Shapiro

We apply our quantum theory of nondegenerate multiwave mixing [ Phys. Rev. A37, 2017 ( 1988)] to squeezed-state generation experiments with two-level atoms. Our main interest is to predict the amount of squeezing achievable with a Doppler-broadened two-level medium. We are particularly interested in the single-beam configuration, in which all four interacting beams are spatially degenerate. We analytically solve the coupled-mode quantum Langevin equations for nondegenerate four-wave mixing. The solutions are used to compute the amount of squeezing. In the computation the effects of pump–probe phase mismatch, collisions, Doppler broadening, and Gaussian-intensity variation are comprehensively taken into account for the first time to our knowledge. Simple rules of thumb as to where one can see squeezing in both degenerate- and nondegenerate-frequency cases are derived by examining the limit of a short medium. We then present the case of an infinitely long medium, in which maximum squeezing is achieved when there is no pump–probe phase mismatch. With the inclusion of pump–probe phase mismatch, however, the maximum amount of squeezing is obtained with a finite-length medium instead. This prompts us to investigate in detail the finite-length medium case. Our results show that the effects of Doppler broadening and Gaussian-intensity variation can be largely circumvented by detuning the pump frequency more than three Doppler half-widths from resonance and that good broadband squeezing can be achieved even with a Doppler-broadened medium that has a moderate amount of collision broadening. Under these circumstances it is found that the effect of pump self-focusing or defocusing will be the major factor that limits the amount of achievable squeezing. In particular, the spatially varying nonlinear refractive indices seen by the pump and the probe modes are quite different, which causes the former to become spatially mismatched with the latter in the region in which strong squeezing is otherwise expected.

Journal of the Optical Society of America B•Jan 1, 1991•10 citations
In this thesis we study three aspects of squeezed light. First, we investigate the generation of pulsed, near‑pure, degenerate, single‑temporal‑mode squeezed light produced by dual‑pump spontaneous four wave mixing in integrated silicon‑nitride coupled‑ring resonators. We show that parasitic spontaneous four wave mixing processes inherent to the dual‑pump configuration can substantially degrade the amount of generated squeezing and state purity. To mitigate these effects we explore pump detuning, engineered dispersion, and an auxiliary‑ring structure as suppression strategies. We then optimize the incident pump amplitude and phase, demonstrating that longer pump pulses can yield highly squeezed, temporally separable states and that an appropriate pre‑chirp tracks the effects of self‑ and cross‑phase modulation, increasing intracavity pump amplitudes and the amount of generated squeezing. Next, we analyze the spectral–temporal structure and photon statistics of strongly correlated squeezed light. We develop a general formalism based on the Whittaker–Shannon interpolation of the joint‑temporal amplitude that is particularly useful in the long‑pulse and continuous‑wave limits, where the instantaneous photon density is low but the total photon number may be large. This packet‑based description provides a local, physically transparent account of the state and its photon statistics that complements the Schmidt decomposition, and extends to nonclassical states for which a Schmidt decomposition is not available. Finally, we examine whether or not squeezed illumination can enhance two‑photon excitation relative to classical light, and whether any enhancement is experimentally detectable. We construct a model including radiative and nonradiative broadening to compute scattered and absorbed energy, and apply it to fluorescence from cesium atoms in a magneto‑optical trap driven by classical and squeezed light in both continuous‑wave and pulsed regimes. Under ideal conditions squeezed light can produce a measurable enhancement in both limits, but the gains are moderate and smaller than some recent molecular reports; additional broadening or loss would further reduce detectability.
We develop a formalism to describe squeezed light with large spectral-temporal correlations. This description is valid in all regimes, but is especially applicable in the long pulse to continuous-wave limit where the photon density at any particular time is small, although the total number of photons can be quite large. Our method relies on the Whittaker-Shannon interpolation formula applied to the joint temporal amplitude of squeezed light, which allows us to ``deconstruct'' the squeezed state. This provides a local description of the state and its photon statistics, making the underlying physics more transparent than does the use of the Schmidt decomposition. The formalism can easily be extended to more exotic nonclassical states where a Schmidt decomposition is not possible.
We develop a formalism to describe squeezed light with large spectral-temporal correlations. This description is valid in all regimes, but is especially applicable in the long pulse to continuous-wave limit where the photon density at any particular time is small, although the total number of photons can be quite large. Our method relies on the Whittaker-Shannon interpolation formula applied to the joint temporal amplitude of squeezed light, which allows us to "take apart" the squeezed state. This provides a local description of the state and its photon statistics, making the underlying physics more transparent than does the use of the Schmidt decomposition. The formalism can easily be extended to more exotic nonclassical states where a Schmidt decomposition is not possible.
Squeezed light is expected to enable new quantum metrology and quantum computation applications, but the very high degree of experimental control required in practice places severe demands on the physical devices used to generate it. As ultrafast squeezed light sources are reaching an unprecedented degree of brightness and modal control, there is a strong interest in developing methods for their experimental characterization and theoretical understanding. In this thesis, we demonstrate both a new application and a new characterization technique for pulsed squeezed light. In the first part of the thesis, we present a new metrological application of pulsed squeezed light: quantum-enhanced label-free nonlinear microscopy. Stimulated emission microscopy (SEM) is a state-of-the-art pump-probe microscopy technique whose sensitivity is ultimately limited by shot noise in the probe beam. We propose to overcome this fundamental limitation by using a sub-Poissonian probe generated via optical parametric amplification. We demonstrate an intensity-squeezed sub-picosecond pulsed probe, and a simple stimulated emission microscope. Using this squeezed probe, sub-Poissonian statistics are observed in the SEM signal. After this proof-of-principle experiment, we aim to provide an improved design for a source of intensity-squeezed light. First, we develop a theoretical framework to simulate the photon statistics of a general sub-Poissonian source, considering pulsed and focused pump and seed fields in a unified spatio-temporal description. Next, we use this framework to suggest possible improvements to our previous squeezed probe. In the second part of this thesis, we provide new theoretical and experimental tools to analyze the high gain regime of pulsed spontaneous parametric down-conversion (SPDC). We study a waveguided source capable of generating twin-beams with tens of photons in a single spatio-temporal mode. We develop a framework to efficiently simulate SPDC for an arbitrary nonlinear gain, including the effect of parasitic nonlinearities such as self-phase modulation (SPM) of the pump and cross-phase modulation (XPM) between pump and twin-beams. We experimentally characterize our source using a new technique based on stimulated difference-frequency generation (DFG). In a type-II down-conversion process, we measure the frequency generation produced not only in the orthogonal polarization to the seeding beam, but also in its same polarization, which we interpret as cascaded difference-frequency generation. We argue that the additional information obtained in this measurement allows for a self-referenced estimation of the squeezing gain. Using these measurements, we accurately fit our theoretical model, revealing that, in the high gain regime, parasitic nonlinearities strongly affect the spectral structure of the twin-beams. We propose a simple strategy to reduce the impact of these nonlinearities on the modal structure of SPDC.
Silicon nitride microresonators driven by strong pump pulses can generate squeezed light in a dominant spectral-temporal mode, a central resource for continuous-variable quantum computation. In the high parametric gain regime, several effects, including self- and cross-phase modulation as well as time-ordering corrections, become significant and can degrade source performance. In this work, we comprehensively investigate the generation of squeezed light from a silicon nitride resonator under pulsed pumping, spanning from low to high parametric gain up to approximately 16 photons/pulse. We experimentally study how the average photon number and the first- and second-order correlations of the squeezed marginal modes evolve with increasing pulse energy, across various frequency detunings and pulse durations. Furthermore, we analyze the errors introduced by multipair emissions in estimating the joint temporal intensity via time-resolved coincidence measurements. We propose and demonstrate an error-correction strategy based on the marginal distributions of time-resolved multiphoton events. Our results provide a practical strategy for optimizing the gain and the temporal mode structure of pulsed squeezed light sources in microresonators, elucidating the physical mechanisms and limitations that govern source performance in the high-gain regime.
We investigate the use of integrated structures for the efficient generation of squeezed light via dual-pump spontaneous four-wave mixing. We consider the case of ring resonators, in which resonant field enhancement is typically used to increase the efficiency of nonlinear interactions. We show that in these structures the presence of a comb of equally spaced resonances can also lead to the enhancement of parasitic processes that can degrade the quality of the generated light, thus limiting the achievable squeezing. Here, we discuss possible solutions to this issue and introduce a device consisting of a ring resonator and a resonant interferometric coupler able to control the field enhancement selectively. We show that through this structure one can strongly limit the effect of parasitic processes and overcome the intrinsic limitations of a single-ring resonator. Finally, we model the effect of nonlinear parasitic processes and provide an analytic expression of the achievable squeezing.
We apply our quantum theory of nondegenerate multiwave mixing [ Phys. Rev. A37, 2017 ( 1988)] to squeezed-state generation experiments with two-level atoms. Our main interest is to predict the amount of squeezing achievable with a Doppler-broadened two-level medium. We are particularly interested in the single-beam configuration, in which all four interacting beams are spatially degenerate. We analytically solve the coupled-mode quantum Langevin equations for nondegenerate four-wave mixing. The solutions are used to compute the amount of squeezing. In the computation the effects of pump–probe phase mismatch, collisions, Doppler broadening, and Gaussian-intensity variation are comprehensively taken into account for the first time to our knowledge. Simple rules of thumb as to where one can see squeezing in both degenerate- and nondegenerate-frequency cases are derived by examining the limit of a short medium. We then present the case of an infinitely long medium, in which maximum squeezing is achieved when there is no pump–probe phase mismatch. With the inclusion of pump–probe phase mismatch, however, the maximum amount of squeezing is obtained with a finite-length medium instead. This prompts us to investigate in detail the finite-length medium case. Our results show that the effects of Doppler broadening and Gaussian-intensity variation can be largely circumvented by detuning the pump frequency more than three Doppler half-widths from resonance and that good broadband squeezing can be achieved even with a Doppler-broadened medium that has a moderate amount of collision broadening. Under these circumstances it is found that the effect of pump self-focusing or defocusing will be the major factor that limits the amount of achievable squeezing. In particular, the spatially varying nonlinear refractive indices seen by the pump and the probe modes are quite different, which causes the former to become spatially mismatched with the latter in the region in which strong squeezing is otherwise expected.