We propose a scheme to realize a cubic quantum nondemolition (QND) Hamiltonian with optical parametric interactions. We show that strongly squeezed fundamental and second-harmonic fields propagating in a χ (2) nonlinear medium effectively evolve under a cubic QND Hamiltonian. We highlight the versatility offered by such a Hamiltonian for engineering non-Gaussian quantum states, such as Schrödinger cat states and cubic phase states. We show that our scheme can be highly tolerant of overall detection inefficiency with an auxiliary high-gain phase-sensitive optical amplifier. Our proposal involves parametric interactions in a mesoscopic photon-number regime, significantly enhancing the effective nonlinear coupling from the native single-photon coupling rate while providing powerful means to fight photon propagation loss. Experimental numbers suggest that our scheme might be feasible in the near future, particularly with pulsed nonlinear nanophotonics.
We propose a scheme to realize a cubic quantum nondemolition (QND) Hamiltonian with optical parametric interactions. We show that strongly squeezed fundamental and second-harmonic fields propagating in a χ (2) nonlinear medium effectively evolve under a cubic QND Hamiltonian. We highlight the versatility offered by such a Hamiltonian for engineering non-Gaussian quantum states, such as Schrödinger cat states and cubic phase states. We show that our scheme can be highly tolerant of overall detection inefficiency with an auxiliary high-gain phase-sensitive optical amplifier. Our proposal involves parametric interactions in a mesoscopic photon-number regime, significantly enhancing the effective nonlinear coupling from the native single-photon coupling rate while providing powerful means to fight photon propagation loss. Experimental numbers suggest that our scheme might be feasible in the near future, particularly with pulsed nonlinear nanophotonics.
We propose a deterministic, measurement-free implementation of a cubic phase gate for continuous-variable quantum information processing. In our scheme, the applications of displacement and squeezing operations allow us to engineer the effective evolution of the quantum state propagating through an optical Kerr nonlinearity. Under appropriate conditions, we show that the input state evolves according to a cubic phase Hamiltonian, and we find that the cubic phase gate error decreases inverse quartically with the amount of quadrature squeezing, even in the presence of linear loss. We also show how our scheme can be adapted to deterministically generate a nonclassical approximate cubic phase state with high fidelity using a ratio of native nonlinearity to linear loss of only 10^{-4}, indicating that our approach may be experimentally viable in the near term even on all-optical platforms, e.g., using quantum solitons in pulsed nonlinear nanophotonics.
We introduce a programmable optical parametric amplifier (OPA) synthesizer that, under a heralded photon-number-resolving framework, generates high-fidelity cubic phase states and amplifies Schrodinger cat states. By systematically exploring both the catalytic configuration, where the idler input and output contain the same number of photons (m=n), and non-catalytic configurations (m=n), we discover two qualitatively different functionalities. First, with a coherent-state signal input, our protocol generates cubic phase states with fidelity exceeding 0.99 across a broad range of (m,n) configurations. Second, using a Schrödinger cat state as the signal input, the same framework amplifies the cat state: an input cat with amplitude αin≤1 is transformed into an output squeezed cat with αout≥2 while maintaining fidelity above 0.99. The catalytic configuration preserves the input parity and restores the idler state, whereas non-catalytic configurations enable parity-flipping amplification with higher success rates. Moreover, the amplified output can serve as a seed for subsequent amplification rounds, offering a self-seeding pathway to progressively larger cat states. Our protocol requires only moderate-gain OPA operation and low-order photon-number-resolving detection, providing a flexible and experimentally accessible platform for cubic phase state preparation and amplified squeezed cat state generation.
Realization of a room-temperature ultrafast photon-number-resolving quantum nondemolition (QND) measurement would have significant implications for photonic quantum information processing, enabling, for example, deterministic quantum computation in discrete-variable architectures, but the requirement for strong coupling has hampered the development of scalable implementations.In this work, we propose and analyze a nonlinear-optical route to photon-number-resolving QND using quadratic (i.e., χ (2) ) nonlinear interactions.We show that the coherent pump field driving a frequency-detuned optical parametric amplifier (OPA) experiences displacements conditioned on the number of signal Bogoliubov excitations.A measurement of the pump displacement thus provides a QND measurement of the signal Bogoliubov excitations, projecting the signal mode to a squeezed photon-number state.We then show how our nonlinear OPA dynamics can be utilized to deterministically generate Gottesman-Kitaev-Preskill states with only additional Gaussian resources, offering an all-optical route for fault-tolerant quantum information processing in continuous-variable systems.Finally, we place these QND schemes into a more traditional context by highlighting analogies between the frequency-detuned optical parametric oscillator and multilevel atom-cavity quantum electrodynamics systems by showing how continuous monitoring of the outcoupled pump quadrature induces conditional localization of the intracavity signal mode onto squeezed photon-number states.Our analysis suggests that our proposal may be viable in near-term χ (2) nonlinear nanophotonics, highlighting the rich potential of the OPA as a universal tool for ultrafast non-Gaussian quantum state engineering and quantum computation.
Realization of quantum nonlinearity in quadratic optomechanics, including optical and mechanical nonlinearity at the single-photon level, is crucial to explore extraordinary quantum features. Here we investigate an exponential enhancement of quadratic optomechanical interaction via parametric amplifications. The parametric process can form an in-phase amplified quadrature, and the rate of coupling to the in-phase quadrature will be exponentially increased even to the single-photon strong-coupling regime. Concretely, to achieve the optical nonlinearity mediated by the quadratic optomechanical interaction, we can employ a mechanical parametric process, and the in-phase mechanical quadrature can strongly couple to the cavity mode, leading to an enhanced optical nonlinearity such as a photon blockade. Similarly, via employing the optical parametric process, the in-phase optical quadrature can also effectively mediate the quadratic interaction, leading to an enhanced mechanical nonlinearity such as mechanical squeezing, bi-excitation exchange interaction and feasibility of quantum non-demolition detection of mechanical motion. However, the parametric process can also enlarge the noise, and a squeezing vacuum with the phase matching condition should be introduced to suppress the same.
Iterative CZ-gate-based protocol for squeezed Schrödinger cat state engineering
Squeezed optical Schrödinger cat states constitute a key resource for both fundamental tests of quantum theory and up-to-date quantum technologies. We propose a measurement-assisted gate for the generation and manipulation of the cat states. In this scheme, an ancilla in the non-Gaussian small-amplitude (in general, squeezed) Schrödinger cat state and the target oscillator initially prepared in a squeezed vacuum (or coherent) state are subjected to a quantum nondemolition (QND) entangling operation followed by projective homodyne measurement. The proposed gate enables generation of high-fidelity squeezed Schrödinger cat states with controllable size and squeezing with tunable fidelity/success-probability trade-off. We also introduce an iterative, homodyne-conditioned CZ-based protocol for cat-state amplification. The parameter regimes required to achieve the desired fidelity and the success probability are analyzed. The approach is well suited for applications in measurement-based quantum computing and hybrid quantum networks where non-Gaussian resources enhance computational and communication capabilities.
We study the emergence of non-Gaussian quantum features in pulsed squeezed light generation with a mesoscopic number (i.e., dozens to hundreds) of pump photons. Due to the strong optical nonlinearities necessarily involved in this regime, squeezing occurs alongside significant pump depletion, compromising the predictions made by conventional semiclassical models for squeezing. Furthermore, nonlinear interactions among multiple frequency modes render the system dynamics exponentially intractable in naïve quantum models, requiring a more sophisticated modeling framework. To this end, we construct a nonlinear Gaussian approximation to the squeezing dynamics, defining a “Gaussian interaction frame” in which non-Gaussian quantum dynamics can be isolated and concisely described using a few dominant (i.e., principal) supermodes. Numerical simulations of our model reveal non-Gaussian distortions of squeezing in the mesoscopic regime, largely associated with signal-pump entanglement. We argue that state of the art in nonlinear nanophotonics is quickly approaching this regime, providing an all-optical platform for experimental studies of the semiclassical-to-quantum transition in a rich paradigm of coherent, multimode nonlinear dynamics. Mesoscopic pulsed squeezing, thus, provides an intriguing case study of the rapid rise in dynamic complexity associated with semiclassical-to-quantum crossover, which we view as a correlate of the emergence of new information processing capacities in the quantum regime.