Indefinite causal order (ICO) has the potential to be a new resource for quantum information processing. In most of its experiments, ICO has been investigated in a photonic platform. Here, we investigate ICO in a cavity quantum electrodynamics system composed of two cavities. Our results show that ICO can create highly entangled states of two distant cavity fields that never interact directly independent of the initial (excited or ground) state of the atom. These entangled states can have the form of one- or two-photon NOON states. We show that ICO can interchange one photon between both cavities without changing the state of the atom, something that is impossible to achieve for two cavities in well-defined order. Furthermore, the vacuum Rabi oscillations either disappear or lose their sinusoidal form with ICO. Our results show the potential that ICO can offer in the paradigm of light-matter interaction for coherently controlling atom-field observables.

Lithium niobate and lithium tantalate see widespread use in optics and electronics, and are increasingly used for cryogenic applications. Despite their broad deployment, their optical band gap and its relation to the crystal stoichiometry are not well characterised as a function of temperature. In this work, we study the optical absorption properties of congruent, stoichiometric, MgO-doped and Er-doped lithium niobate as well as congruent lithium tantalate across the temperature range between 7 K and 1000 K by means of optical transmission spectroscopy. Our results demonstrate that the difference of the optical band gap typically observed at room temperature between different stoichiometries is not primarily attributable to the intrinsic electronic structure, but rather to different electron-phonon couplings and the average phonon energies. Additionally, we exemplarily study the temperature shift of the 523 nm absorption line in Er-doped lithium niobate due to the increased interest in optically active dopants. To facilitate future analyses, we present the open-source software suite PhoQS-Treat (Tauc Regression Edge Analysis Tool), which enables automated Tauc regressions alongside additional analytical capabilities. This work advances the development of high-performance lithium niobate-based devices.

Lithium niobate sees widespread use in nonlinear and quantum optical devices, such as for sum- and difference-frequency generation or spontaneous parametric downconversion. In lithium niobate waveguides, nonlinear optical processes are often limited by the so-called photorefractive effect, which limits the maximum input or output powers and impacts the nonlinear spectral response. Therefore, strategies for the management of photorefractive damage are a key consideration in device design. Usually, the photorefractive damage threshold, i.e., the maximal permissible operating power, can be increased by high-temperature operation of devices. This approach, however, is not applicable in cryogenic environments, which may be required for specialized applications. To better understand the impact of photorefraction in nonlinear optical applications, we study the impact of photorefraction on the phase-matching spectra of two nonlinear-optical sum-frequency generation experiments at (1) high temperatures and (2) cryogenic temperatures. Furthermore, we present an approach to reduce the impact of photorefraction, which is compatible with cryogenic operation. This comprises an auxiliary light source, propagating in the same waveguide, which is used to restore phase-matching spectra impacted by photorefraction, as well as reduce pyroelectric effects. Our work provides an alternative route to photorefraction management applicable to cryogenic environments, as well as in situations with tight energy budgets, such as space applications.

Superconducting nanowire single-photon detectors (SNSPDs) can enable photon-number resolution (PNR) based on accurate measurements of the detector’s response time to few-photon optical pulses. In this work, we investigate the impact of the optical pulse shape and duration on the accuracy of this method. We find that Gaussian temporal pulse shapes yield cleaner arrival-time histograms and, thus, more accurate PNR, compared to bandpass-filtered pulses of equal bandwidth. For low system jitter and an optical pulse duration comparable to the other jitter contributions, photon numbers can be discriminated in our system with a commercial SNSPD. At 60 ps optical pulse duration, photon-number discrimination is significantly reduced. Furthermore, we highlight the importance of using the correct arrival-time histogram model when analyzing photon-number assignment. Using exponentially modified Gaussian distributions, instead of the commonly used Gaussian distributions, we can more accurately determine photon-number misidentification probabilities. Finally, we reconstruct the positive operator-valued measures of the detector, revealing sharp features that indicate the intrinsic PNR capabilities.

Nonclassicality, defined in the quantum optical sense, serves as a resource for photon-based quantum technologies. Therefore, certifying the nonclassicality of a quantum state is crucial for gauging its potential for quantum advantage. However, traditional nonclassicality witnesses that assume perfect knowledge of the witness observables often fail in realistic scenarios with limited statistics and finite-resolution photon detectors. Furthermore, these witnesses do not exploit the fact that certain states are unlikely to be observed in a given experiment. Here, we train a variational model to distinguish classical from nonclassical states using finitely many measurement samples of multimode quantum states that are probed with different photon-number-resolving detection schemes. The learned decision rule is then an indicator of nonclassicality, tailored to a given set of physically relevant states. Our approach is both data-driven and interpretable in the sense that the learned analytical decision rule can be extracted. Training the model on experimental data measured with (i) a superconducting nanowire single-photon detector and (ii) a time-bin multiplexing detection scheme demonstrates the versatility of the approach, paving the way for efficient nonclassicality detection.

Photon counting is a cornerstone of quantum optics. Here, we demonstrate precisely counting from 0 to over 9000 photons, beating the Poisson noise limit by at least 4.1 dB across this range. We achieve sub-single-photon precision up to 276 photons per pulse. To do so, we multiplex eight intrinsically photon-number-resolving superconducting nanowire single-photon detectors across 128 temporal modes. We use a model-informed characterization of each of the 1024 detection bins, for optimal precision. We perform quantum detector tomography to reconstruct the positive operator valued measures (POVMs) of the complete device, which consists of 1.38·10^8 matrix elements. At the repetition rate of our experiment of 80 kHz, we can precisely count photons corresponding to an optical power of approximately 71 pW, bridging the gap from single-photon measurements to high-sensitivity optical power meters. A photon-number-resolving detector of this size, and the tools used to analyze it, will become increasingly important to characterize large quantum states, as well as tasks in precision metrology and optical power standards.

We address the problem of measuring nonclassicality in continuous-variable bosonic systems without having access to a known reference signal. To this end, we construct broader classes of criteria for nonclassicality which allow us to investigate quantum phenomena regardless of the quantumness of selected subsystems. Such witnesses are based on the notion of partial normal ordering. This approach is applied to balanced homodyne detection using arbitrary, potentially nonclassical local oscillator states, yet only revealing the probed signal's quantumness. Our framework is compared to standard techniques, and the robustness and advanced sensitivity of our approach is shown. Therefore, a widely applicable framework, well-suited for applications in quantum metrology and quantum information, is derived to assess the quantum features of a photonic system when a well-defined coherent laser as a reference state is not available in the physical domain under study.

Cointegration of heralded single-photon generation and on-chip detection requires the ability to differentiate between pump light and single photons. We explored the dispersion-induced temporal separation of optical pulses to reach this goal. Our method exploits the distinct group velocities of pump light and single photons, as well as single-photon detectors with high timing resolution. We simulate the propagation for photon pair generation by spontaneous parametric down-conversion in titanium in-diffused waveguides in lithium niobate and thin-film lithium niobate, and spontaneous four-wave mixing in silicon on insulator and silicon nitride. For the different integration platforms, we show the propagation distance required to sufficiently distinguish between pump and single photons for different timing resolutions, and demonstrate that this should be feasible with current superconducting nanowire single-photon detector technologies. Finally, we experimentally simulate our approach using the dispersion in the optical fiber.

By analyzing the physics of multi-photon absorption in superconducting nanowire single-photon detectors (SNSPDs), we identify physical components of jitter. From this, we formulate a quantitative physical model of the multi-photon detector response which combines local detection mechanism and local fluctuations (hotspot formation and intrinsic jitter) with thermoelectric dynamics of resistive domains. Our model provides an excellent description of the arrival-time histogram of a commercial SNSPD across several orders of magnitude, both in arrival-time probability and across mean photon number. This is achieved with just three fitting parameters: the scaling of the mean arrival time of voltage response pulses, as well as the Gaussian and exponential jitter components. Our findings have important implications for photon-number-resolving detector design, as well as applications requiring low jitter such as light detection and ranging (LIDAR).

We perform a feedforward operation at cryogenic temperatures using a multipixel SNSPD, electronic logic and cryogenic lithium niobate modulator. By operating all components in the same cryostat we achieve a latency of (23 ± 3) ns.

The titanium in-diffused lithium niobate waveguide platform is well-established for reliable prototyping and packaging of many quantum photonic components at room temperature. Nevertheless, compatibility with certain quantum light sources and superconducting detectors requires operation under cryogenic conditions. We characterize alterations in phase-matching and mode guiding of a non-degenerate spontaneous parametric down-conversion process emitting around 1556 nm and 950 nm, under cryogenic conditions. Despite the effects of pyroelectricity and photorefraction, the spectral properties match our theoretical model. Nevertheless, these effects cause small but significant variations within and between cooling cycles. These measurements provide a first benchmark against which other nonlinear photonic integration platforms, such as thin-film lithium niobate, can be compared.

Modulation conditioned on measurements on entangled photonic quantum states is a cornerstone technology of optical quantum information processing. Performing this task with low latency requires combining single-photon-level detectors with both electronic logic processing and optical modulation in close proximity. In the technologically relevant telecom wavelength band, detection of photonic quantum states is best performed with high-efficiency, low-noise, and high-speed detectors based on the photon-induced breakdown of superconductivity. Therefore, using these devices for feedforward requires mutual compatibility of all components under cryogenic conditions. Here, we demonstrate low-latency feedforward using a quasi-photon-number-resolved measurement on a quantum light source. Specifically, we use a multipixel superconducting nanowire single-photon detector, amplifier, logic, and an integrated electro-optic modulator in situ below 4K. We modulate the signal mode of a spontaneous parametric down-conversion source, conditional on a photon-number measurement of the idler mode, with a total latency of (23+/-3)ns. The photon-number discrimination actively manipulates the signal mode photon statistics, which is itself a central component in photonic quantum computing reliant on heralded single-photon sources. This represents an important benchmark for the fastest quantum photonic feedforward experiments comprising measurement, amplification, logic and modulation. This has direct applications in quantum computing, communication, and simulation protocols.

Interfacing single-photon detectors with active photonic components is a cornerstone photonic quantum technology. We describe how the output signal of commercial superconducting nanowire single-photon detectors can be used in situ to drive photonic components such as lasers and electro-optic modulators, co-located in the cryostat. This is enabled by developing custom circuitry using cryogenic-compatible discrete components in the SiGe-BiCMOS platform. We have demonstrated this with a number of experiments, in particular optical readout of an SNSPD and low-latency feed-forward modulation based on single-photon measurement events, all at or below 4 K. This manuscript is an abridged version of the Master thesis of the primary author N. Lamberty.

At large scales, quantum systems may become advantageous over their classical counterparts at performing certain tasks. Developing tools to analyse these systems at the relevant scales, in a manner consistent with quantum mechanics, is therefore critical to benchmarking performance and characterising their operation. While classical computational approaches cannot perform like-for-like computations of quantum systems beyond a certain scale, classical high-performance computing (HPC) may nevertheless be useful for precisely these characterisation and certification tasks. By developing open-source customised algorithms using high-performance computing, we perform quantum tomography on a megascale quantum photonic detector covering a Hilbert space of $10^6$. This requires finding $10^8$ elements of the matrix corresponding to the positive operator valued measure (POVM), the quantum description of the detector, and is achieved in minutes of computation time. Moreover, by exploiting the structure of the problem, we achieve highly efficient parallel scaling, paving the way for quantum objects up to a system size of $10^{12}$ elements to be reconstructed using this method. In general, this shows that a consistent quantum mechanical description of quantum phenomena is applicable at everyday scales. More concretely, this enables the reconstruction of large-scale quantum sources, processes and detectors used in computation and sampling tasks, which may be necessary to prove their nonclassical character or quantum computational advantage.

In this paper we briefly review the state-of-the-art of intrinsic photon-number resolution (PNR) with superconducting nanowire single-photon detectors (SNSPDs) and will provide an overview of the various experimental techniques employed to achieve PNR. Additionally, we introduce a resolvability criterion to PNR based on SNSPDs.

Decomposing complex unitary evolution into a series of constituent components is a cornerstone of practical quantum information processing. While the decompostion of an $n\times n$ unitary into a series of $2\times2$ subunitaries is well established (i.e. beamsplitters and phase shifters in linear optics), we show how this decomposition can be generalised into a series of $m\times m$ multimode devices, where $m>2$. If the cost associated with building each $m\times m$ multimode device is less than constructing with $\frac{m(m-1)}{2}$ individual $2\times 2$ devices, we show that the decomposition of large unitaries into $m\times m$ submatrices is is more resource efficient and exhibits a higher tolerance to errors, than its $2\times 2$ counterpart. This allows larger-scale unitaries to be constructed with lower errors, which is necessary for various tasks, not least Boson sampling, the quantum Fourier transform and quantum simulations.

When integrating superconducting detectors on lithium niobate, pyroelectricity can cause irreversible damage to the superconducting films. We investigate several schemes to overcome this issue including different detector designs, coatings and shorting schemes.

Lithium niobate serves as a key quantum photonics integration platform, hosting cryogenic quantum optical devices such as SNSPDs and quantum dots. We explore the impact of pyroelectricity in the cryogenic environment in lithium niobate waveguides.

Lithium niobate has emerged as a promising platform for integrated quantum optics, enabling efficient generation, manipulation, and detection of quantum states of light. However, integrating single-photon detectors requires cryogenic operating temperatures, since the best performing detectors are based on narrow superconducting wires. While previous studies have demonstrated the operation of quantum light sources and electro-optic modulators in LiNbO _3 at cryogenic temperatures, the thermal transition between room temperature and cryogenic conditions introduces additional effects that can significantly influence device performance. In this paper, we investigate the generation of pyroelectric charges and their impact on the optical properties of lithium niobate waveguides when changing from room temperature to 25 K, and vice versa. We measure the generated pyroelectric charge flow and correlate this with fast changes in the birefringence acquired through the Sénarmont-method. Both electrical and optical influence of the pyroelectric effect occur predominantly at temperatures above 100 K.

We demonstrate an opto-electronic operation of an SNSPD at 1K, utilizing a photodiode bias and a cryogenic laser for signal-readout. The cryogenic photonic link reduces the heatload and maintains a high performance of the SNSPD.