Characterizing macroscopic quantum states of light is a frontier challenge at the interface of quantum optics and high-intensity photonics. Here, we demonstrate the first, to our knowledge, direct phase-space tomography of a bright, ultrafast quantum state. We adapt a single-shot f-2f interferometer to sample the Husimi Q-function of a 25 fs bright squeezed vacuum (BSV) pulse (mean photon number N ∼10 12 ) subject to Kerr nonlinearity. Our measurement reveals a clear transformation from a Gaussian distribution with pronounced quadrature antisqueezing to a characteristic "S"-shaped profile as the intensity-dependent nonlinear phase increases. Crucially, we show theoretically that despite optical loss, the state does not degrade into classically modulated light but is rigorously described as a statistical mixture of squeezed coherent states. While global Wigner negativity is masked by technical noise, our results show theoretically that the constituent states individually retain strong Wigner-negative features. This work bridges quantum optics and high-intensity photonics, establishing a platform for diagnosing bright quantum resources.
Characterizing macroscopic quantum states of light is a frontier challenge at the interface of quantum optics and high-intensity photonics. Here, we demonstrate the first, to our knowledge, direct phase-space tomography of a bright, ultrafast quantum state. We adapt a single-shot f-2f interferometer to sample the Husimi Q-function of a 25 fs bright squeezed vacuum (BSV) pulse (mean photon number N ∼10 12 ) subject to Kerr nonlinearity. Our measurement reveals a clear transformation from a Gaussian distribution with pronounced quadrature antisqueezing to a characteristic "S"-shaped profile as the intensity-dependent nonlinear phase increases. Crucially, we show theoretically that despite optical loss, the state does not degrade into classically modulated light but is rigorously described as a statistical mixture of squeezed coherent states. While global Wigner negativity is masked by technical noise, our results show theoretically that the constituent states individually retain strong Wigner-negative features. This work bridges quantum optics and high-intensity photonics, establishing a platform for diagnosing bright quantum resources.
Non-Gaussian states of light are a critical resource for fault-tolerant quantum computing and enhanced metrology, but are typically faint and often obtained via post-selection. Here, we demonstrate the deterministic generation of a bright non-Gaussian state by introducing a Kerr nonlinearity to a macroscopic state of light called bright squeezed vacuum (BSV). To characterize the resulting state, we use a single-shot f-2f interferometer to sample its Husimi function. We observe a clear transformation from a 2D Gaussian distribution to an 'S'-shaped non-Gaussian profile, which is the direct statistical evidence of the intensity-dependent nonlinear phase. The negativity of the Wigner function, which is an intrinsic property of any pure non-Gaussian state, cannot be observed because BSV is a mixed state even under minute optical loss. However, we show that BSV can be considered as a mixture of pure squeezed coherent states, for some of which Kerr-induced Wigner-function negativity is quite tolerant to loss. This work bridges the gap between quantum optics and ultrafast nonlinear optics, opening a path to quantum applications that require high photon flux.
Abstract We theoretically investigate the nonlinear spectral broadening of bright squeezed vacuum (BSV) driven by Kerr nonlinearity in bulk sapphire and demonstrate a route toward generating ultrafast broadband BSV-based light. By analyzing the spectral evolution and frequency correlations during nonlinear propagation, we show that the intrinsic photon-number fluctuations sampled from the BSV input significantly enhance ensemble-averaged spectral broadening compared with coherent pulses of the same mean intensity. Quantum statistics enter through Husimi-Q sampling of the incident squeezed-vacuum state, whereas each realization is subsequently propagated as a semiclassical complex envelope. The generated broadband field exhibits strong photon-number and intensity correlations across a wide spectral range together with excellent temporal compressibility. After a common dispersion compensation, the source supports single-shot pulse durations ranging from approximately 7 fs to 70 fs. This work combines ultrafast temporal characteristics with quantum-originated input statistics in a single optical platform and may provide new opportunities for strong-field quantum optics, including high-harmonic generation and attosecond science.
High-harmonic generation (HHG) is a prototypical strong-field process in which intense light drives matter to emit radiation at integer multiples of the driving frequency. Extending HHG into the quantum-optical regime offers new opportunities to probe and control strongly nonlinear light-matter interactions using nonclassical states of light. Yet describing this regime requires a fully quantum treatment of the correlated electron-photon dynamics, which becomes computationally challenging for broadband, strongly squeezed fields. Here we solve the quantum-electrodynamical dynamics of a two-level system driven by bright squeezed vacuum in a converged multimode Hilbert space. Both the driving field and emitted harmonics are fully quantized, with the light-matter interaction treated nonperturbatively. This enables direct access to the multimode quantum state and its higher-order correlations beyond semiclassical sampling or perturbative descriptions. We show that squeezed-vacuum driving produces harmonic emission with qualitatively distinct second- and third-order photon correlations compared with coherent excitation. Moreover, back-action from the driven emitter strongly reshapes the incident squeezed field, generating pronounced Wigner-function negativities that evolve on attosecond timescales. Our results establish a fully quantum framework for broadband strong-field dynamics with squeezed light and provide a route to predicting and interpreting quantum-HHG experiments and their extension to more complex emitters.
Strong-field physics uses intense optical fields to probe and control electron motion on ultrafast timescales. Recent advances in bright squeezed vacuum have brought macroscopic quantum states of light into the ultrafast strong-field regime, opening prospects for high-harmonic generation and photoionization. Yet linking its phase-space structure to subcycle electron dynamics remains challenging. Here, we demonstrate strong-field tunneling ionization of xenon using a phase-referenced combination of coherent and squeezed fields, with the coherent field defining the ionization clock and quadrature fluctuations of the zero-mean squeezed field providing control. The squeezed field selectively modulates atomic tunneling barriers and electron wave packets, imprinting signatures on photoelectron momentum distributions, number statistics, and energy spectra. Using coincidence measurements of photon number and phase-sensitive photoelectron momentum distributions, we perform quantum state tomography of the driving field by reconstructing its Wigner function. These results establish a bidirectional interface between quantum optics and nonperturbative strong-field electron dynamics, in which the driving quantum field shapes subcycle electron motion while photoionization provides a phase-sensitive probe of the field's quantum state. This work opens new routes toward controlling electron dynamics with quantum light and phase-sensitive quantum state metrology through ultrafast strong-field electron dynamics.
The fascinating nature of light has driven many discoveries in physics, from the theory of special relativity to quantum mechanics. As a carrier of information, light is at the core of high-speed communication over the internet and facilitates the study of numerous physical properties of materials by the interaction of light and matter. Advances in generating and detecting ultrashort light pulses enabled the spectroscopic investigation of matter with unprecedented detail. Meanwhile, the development of more precise and sensitive measurements, leveraging quantum properties of light, has expanded the experimental frontiers of the physical world. Naturally, the question arises: Could the combination of these two breakthroughs push the frontiers even further? A promising candidate to achieve this combination is electro-optic sampling, an electromagnetic-field measurement comprising an up-conversion and a phase-space measurement based on homodyne detection. While it is predominantly used in classical terahertz time-domain spectroscopy, the high sensitivity and spatio-temporal resolution of electro-optic sampling recently enabled the detection of vacuum fluctuations in the ground state of the electromagnetic field by probing an adjustable space-time volume. Yet, the generation and characterization of more intricate quantum pulses on ultrafast timescales is still challenging, especially in the terahertz frequencies. Exploiting the quantum properties of a light pulse over a broad frequency range requires sophisticated knowledge about the prepared quantum pulse as well as the measurement setup at use. However, Heisenberg's uncertainty relation fundamentally prevents the complete determination of an arbitrary quantum state from a single measurement. Instead, the quantum state has to be reconstructed from the statistics of many measurements — a process known as quantum state tomography. In this thesis, we establish the theoretical foundations for a comprehensive tomographic reconstruction of pulsed quantum states of light, encompassing both the statistics and dynamics of the state. Additionally, we introduce tools to simplify the description of the nonlinear interaction underlying electro-optic sampling and in turn the tomography setups presented here. As a first step, we investigate the application of electro-optic sampling to the time-local reconstruction of various pulsed quantum states of light on ultrafast timescales. We identify two types of noise, which impact the quality of the reconstruction: shot noise, arising from the nonlinear interaction in electro-optic sampling, and thermal noise, due to the localization of the (correlated) quantum state within a small space-time volume during the measurement. To improve the reconstruction, we propose to use a strong probe pulse, suppressing the shot noise, and to select an appropriate detection frequency band, reducing thermal noise. Thus, the proposed tomography enables the characterization of quantum states in terahertz frequency range on ultrafast timescales. However, the time-local nature of the measurement imposes a trade-off between the reconstruction of the quantum state in phase space and the time domain. In a second step, we propose a reconstruction method based on two-time field-correlation measurement, which we call correlation tomography, able to overcome the restriction to time-local states. While the tomography of quantum states in an optimal pulse basis has been demonstrated, it requires prior knowledge about the temporal structure of the quantum state. We introduce an algorithm for reconstructing high-dimensional multimode Gaussian quantum states, which are completely characterized by the covariance matrix of the quadratures of fully distinguishable pulses. The reconstruction is achieved by orthogonalizing the overlapping time windows of the correlation measurement in post-processing. We compare a homodyne-based implementation to electro-optic sampling and develop an optimization scheme for the latter, to mitigate the shot noise in the non-perturbative regime of strong nonlinear interactions. Furthermore, we derive the full-counting statistics of the field-correlation measurement and theoretically demonstrate the reconstruction of pulsed Fock states. This opens an avenue to the full tomography of highly multimode non-Gaussian states. In the third and last step, we derive a formalism to simplify the description of the up-conversion required in electro-optic sampling. If a pulsed quantum states is up-converted and localized in a small space-time region, the transformation of the localized modes during the nonlinear interaction corresponds to an open quantum system, rendering the standard tools of quantum optics inapplicable. By introducing the generalized Bloch-Messiah decomposition, we simplify the input-output relation of the nonlinear interaction to a set of effective modes relevant for subsequent processing, such as detection. Using this framework, we derive an analytic phase-space input-output relation for the nonlinear interaction of pulsed quantum states, applicable to open quantum systems. We study the resulting dynamics using two example input states: a Fock state and a two-mode squeezed state. Based on the von Neumann entropy of the output state, we develop an intuitive understanding of the generalized Bloch-Messiah decomposition. The rich structure of pulsed quantum states of light can be a powerful resource, but also challenging to operate with, in theory as well as in experiment. The characterization methods and theoretical tools developed in this thesis, tailored to pulsed quantum light and the nonlinear interaction thereof, can pave the way to the application of this resource to fundamental research as well as quantum technologies.
Abstract Bright squeezed vacuum (BSV) has emerged as a macroscopic nonclassical light source capable of driving strong-field processes. Yet its broad, long-tailed photon-number distribution bears little resemblance to the narrow poissonian distribution of a coherent field, obscuring how the corresponding strong-field responses are connected. We show that field-quadrature space supplies the missing continuous description: coherent, squeezed coherent, and BSV states are Gaussian wave packets distinguished only by their centers and widths. This representation provides a unified framework for tracing the coherent-to-BSV transition at fixed mean photon number and for analyzing both ionization yields and photoelectron spectra. Crucially, BSV is a symmetry-protected endpoint in quadrature space. Near the BSV limit, we identify a simple scaling law of the ionization response associated with a residual coherent component. We show that this scaling arises from parity-induced stationarity with respect to the Gaussian center, together with the accompanying width variation near the BSV limit. The result provides a symmetry-based criterion for approaching the BSV regime and a potential probe of a mode-matched coherent displacement through the strong-field response itself.