We investigate the preparation of frequency-tunable photonic Fock states in a hybrid cavity system consisting of a nonlinear medium and a two-level system. Employing a gradient-based optimization approach, we construct multipulse driving protocols that control the system dynamics through pulse amplitudes, phases, and inter-pulse delays. Assuming unitary dynamics, the optimized sequences enable near-deterministic preparation of low-photon-number Fock states. We extend the optimization framework to open-system dynamics by modeling atomic decay and photon loss within the Lindblad master equation. This allows us to identify pulse sequences that exhibit enhanced robustness against dissipation compared to those optimized under idealized assumptions. Furthermore, we find that optimal pulse sequences obey strict constraints on relative phases, which are limited to values of 0 or $π$. These phase restrictions are supported by an analytical study that investigates a simple two-pulse sequence treating the second pulse perturbatively.
We investigate the preparation of frequency-tunable photonic Fock states in a hybrid cavity system consisting of a nonlinear medium and a two-level system. Employing a gradient-based optimization approach, we construct multipulse driving protocols that control the system dynamics through pulse amplitudes, phases, and inter-pulse delays. Assuming unitary dynamics, the optimized sequences enable near-deterministic preparation of low-photon-number Fock states. We extend the optimization framework to open-system dynamics by modeling atomic decay and photon loss within the Lindblad master equation. This allows us to identify pulse sequences that exhibit enhanced robustness against dissipation compared to those optimized under idealized assumptions. Furthermore, we find that optimal pulse sequences obey strict constraints on relative phases, which are limited to values of 0 or π. These phase restrictions are supported by an analytical study that investigates a simple two-pulse sequence treating the second pulse perturbatively.
We propose a scheme for quantum-light generation in a nonlinear cavity hybridized with a two-level system and theoretically show that, when excited by a series of controlled pump pulses, the hybrid source generates Fock states with high probabilities, e.g., one- and two-photon states can be generated near on demand, and Fock states with up to seven photons with a probability above 50%. The tailorable nature of the nonlinear cavity allows for generating Fock states with arbitrary frequencies, even with a fixed two-level system, creating fundamentally new opportunities in all areas of quantum technologies.
In this work, we develop a coherent control technique for cavity QED based on amplitude amplification. We consider two physical platforms. In the first setting, we study a three-level quantum emitter coupled to a single mode of an optical cavity and introduce a protocol for producing traveling single photons based on oblivious amplitude amplification. As the key ingredient of our protocol, we propose an extension of oblivious amplitude amplification which uses reflection unitaries solely on the signal qubit, along with U and U†, where the unitary U prepares the initial state. Our approach improves the scaling of the single-photon-generation protocol length from N∼1/p to N∼1/p, with p denoting the success probability of obtaining a short single photon from a single application of the weak control pulse. Furthermore, our protocol also reduces the error from intrinsic cavity loss compared to protocols using a single strong control pulse in various experimentally relevant regimes, suggesting the application of our methods for error reduction. In the second setting, we consider a superconducting qubit coupled to a single bosonic mode of a microwave cavity in a circuit QED architecture in the dispersive regime for preparing Fock states. Using fixed-point amplitude amplification, we obtain a protocol for preparing Fock states whose length scales as O(n1/4), where n is the number of photons. Additionally, as an application of our methods for state preparation, we describe a protocol for preparing NOON states.
Interactions between photons (nonlinearities) enable a powerful form of control over the state of light. This control has enabled technologies such as light sources at new wavelengths, ultra-short optical pulses, frequency-comb metrology systems, even quantum light sources. Common to a wide variety of nonlinear optical technologies is an equilibrium between an energy source, such as an external laser, and dissipation, such as radiation loss or absorption. In the vast majority of these systems, the coupling between the system and the outside world (which leads to loss) is well-described as ``Markovian,'' meaning that the outside world has no memory of its past state. In this work, we introduce a class of driven-dissipative systems in which a nonlinear cavity experiences non-Markovian coupling to the outside world. In the classical regime, we show that these non-Markovian cavities can have extremely low thresholds for nonlinear effects, as well as self-pulsing instabilities at THz rates, and rich phase diagrams with alternating regions of stability and instability. In the quantum regime, we show how these system, when implemented on state-of-the-art platforms, can enable generation of strongly squeezed cavity states with intensity fluctuations that can be more than 15 dB below the classical limit, in contrast to the Markovian driven-dissipative cavity, in which the limit is 3 dB. In the regime of few-photon nonlinearity, such non-Markovian cavities can enable a deterministic protocol to generate Fock states of high order, which are long-desired, but still elusive at optical frequencies. We expect that exploiting non-Markovian couplings in nonlinear optics should in the future lead to even richer possibilities than those discussed here for both classical and quantum light manipulations.
Interactions between photons (nonlinearities) enable a powerful form of control over the state of light. This control has enabled technologies such as light sources at new wavelengths, ultra-short optical pulses, frequency-comb metrology systems, even quantum light sources. Common to a wide variety of nonlinear optical technologies is an equilibrium between an energy source, such as an external laser, and dissipation, such as radiation loss or absorption. In the vast majority of these systems, the coupling between the system and the outside world (which leads to loss) is well described as “Markovian,” meaning that the outside world has no memory of its past state. In this work, we introduce a class of driven-dissipative systems in which a nonlinear cavity experiences non-Markovian coupling to the outside world. In the classical regime, we show that these non-Markovian cavities can have extremely low thresholds for nonlinear effects, as well as self-pulsing instabilities at THz rates, and rich phase diagrams with alternating regions of stability and instability. In the quantum regime, we show how these systems, when implemented on state-of-the-art platforms, can enable generation of strongly squeezed cavity states with intensity fluctuations that can be more than 15 dB below the classical limit, in contrast to the Markovian driven-dissipative cavity, in which the limit is 3 dB. In the regime of few-photon nonlinearity, such non-Markovian cavities can enable a deterministic protocol to generate Fock states of high order, which are long-desired, but still elusive at optical frequencies. We expect that exploiting non-Markovian couplings in nonlinear optics should in the future lead to even richer possibilities than those discussed here for both classical and quantum light manipulations.
We propose a mechanism for producing Fock states on demand leaking from a single mode optical cavity interacting with a single atom and a laser pulse. The number of photons can be chosen, as it is determined by the Zeeman substructure of the ground state of the atom and its initial state. The deterministic generation of a free-propagating Fock state of 1≤n≤2F photons is achieved, when a circularly polarized laser pulse completely transfers the atomic population between Zeeman sublevels of the ground hyperfine state F through far-detuned Raman scattering thus producing linearly polarized cavity photons. We describe analytically the evolution of optical field taking into account the spontaneous losses and the cavity damping. We demonstrate the possibility of production of Fock-state with different numbers of photons by using different transitions of the same atom. We show also that this technique provides a deterministic source of a train of identical multiphoton Fock-states, if a sequence of left- and right-circularly polarized laser pulses is applied. The resulting states have potential applications in quantum computation and simulation.
We propose a fast laser pulse sequence for the generation of non-thermal Fock state mixtures of the motion of a trapped ion, targeted at displacement metrology beyond the standard quantum limit. Using a polaron-frame description of the ion-laser interaction, we identify a resonant operating point-zero detuning and a Rabi frequency matching the trap frequency-at which selective population trapping survives strong driving, enabling preparation speeds beyond the weak-driving limit of previous protocols without requiring ground-state cooling. We trace the residual infidelity at large Lamb-Dicke parameter η to a single coherent process, the counter-rotating blue-sideband term neglected in the rotating-wave approximation, and show that it is suppressed by two routine calibrations: a percent-level refocusing of the pulse duration and a small compensating Bloch-Siegert detuning. Numerical simulations of the full sequence show that this refinement keeps the preparation error at or below the 10% level up to η≈0.5 and restores the displacement-sensing Fisher information that the uncorrected protocol loses at strong coupling, recovering up to 9 dB relative to the nominal sequence.