Quantum states are important resources and their preparations are essential prerequisites to all quantum technologies. However, they are extremely fragile due to the inevitable dissipations. Here the all-optical generation of a deterministic squeezed Schr\"odinger-cat state based on dissipation is proposed. Our system is based on the Fredkin-type interaction between three optical modes, one of which is subject to coherent two-photon driving and the others are coherent driving. We show that an effective degenerate three-wave-mixing process can be engineered in our system, which can cause the simultaneous loss of two photons, resulting in the generation of a deterministic squeezed Schr\"odinger-cat state. More importantly, by controlling the driving fields in our system, the two-photon loss can be adjustable, which can accelerate the generation of squeezed Schr\"odinger-cat states. In addition, we exploit the squeezed Schr\"odinger-cat states to estimate the phase in the optical interferometer and show that the quantum Fisher information about the phase can reach the Heisenberg limit in the limit of a large photon number. Meanwhile, it can have an order of magnitude factor improvement over the Heisenberg limit in the low-photon-number regime, which is very valuable for fragile systems that cannot withstand large photon fluxes. This work proposes an all-optical scheme to deterministically prepare the squeezed Schr\"odinger-cat state with high speed and can also be generalized to other physical platforms.
Quantum states are important resources and their preparations are essential prerequisites to all quantum technologies. However, they are extremely fragile due to the inevitable dissipations. Here the all-optical generation of a deterministic squeezed Schr"odinger-cat state based on dissipation is proposed. Our system is based on the Fredkin-type interaction between three optical modes, one of which is subject to coherent two-photon driving and the others are coherent driving. We show that an effective degenerate three-wave-mixing process can be engineered in our system, which can cause the simultaneous loss of two photons, resulting in the generation of a deterministic squeezed Schr"odinger-cat state. More importantly, by controlling the driving fields in our system, the two-photon loss can be adjustable, which can accelerate the generation of squeezed Schr"odinger-cat states. In addition, we exploit the squeezed Schr"odinger-cat states to estimate the phase in the optical interferometer and show that the quantum Fisher information about the phase can reach the Heisenberg limit in the limit of a large photon number. Meanwhile, it can have an order of magnitude factor improvement over the Heisenberg limit in the low-photon-number regime, which is very valuable for fragile systems that cannot withstand large photon fluxes. This work proposes an all-optical scheme to deterministically prepare the squeezed Schr"odinger-cat state with high speed and can also be generalized to other physical platforms.
Quantum states of light, particularly at optical frequencies, are considered necessary to realize a host of important quantum technologies and applications, spanning Heisenberg-limited metrology, continuous-variable quantum computing, and quantum communications. Nevertheless, a wide variety of important quantum light states are currently challenging to deterministically generate at optical frequencies. In part, this is due to a relatively small number of schemes that prepare target quantum states given nonlinear interactions. Here, we present an especially simple concept for deterministically generating and stabilizing important quantum states of light, using only third-order optical nonlinearities and engineered dissipation. We show how, by considering either a nonlinear cavity with frequency-dependent outcoupling or a chain of nonlinear waveguides, one can induce high loss for all but some desired light intensities. Specifically, we find that the stabilized intensities can correspond to an evenly spaced pattern of stablilized photon numbers. This is shown to produce important quantum states with coherent superpositions between various photon numbers. As examples of this phenomenon, we show cavities which can stabilize squeezed states, as well as produce "photon-number-comb" states. Moreover, in these types of filter cavities, Glauber coherent states will deterministically evolve into Schrodinger cat states of a desired order. We discuss potential realizations in quantum nonlinear optics. More broadly, we expect that combining the techniques introduced here with additional "phase-sensitive" nonlinearities (such as second-order nonlinearity) should enable passive stabilization and generation of a wider variety of states than shown here.
Quantum states of light, particularly at optical frequencies, are considered necessary to realize a host of important quantum technologies and applications, spanning Heisenberg-limited metrology, continuous-variable quantum computing, and quantum communications. Nevertheless, a wide variety of important quantum light states are currently challenging to deterministically generate at optical frequencies. In part, this is due to a relatively small number of schemes that prepare target quantum states given nonlinear interactions. Here, we present an especially simple concept for deterministically generating and stabilizing important quantum states of light, using only simple third-order optical nonlinearities and engineered dissipation. We show how by considering either a nonlinear cavity with frequency-dependent outcoupling, or a chain of nonlinear waveguides, one can "filter" out all but a periodic ladder of photon number components of a density matrix. As examples of this phenomenon, we show cavities which can stabilize squeezed states, as well as produce "photon-number-comb" states. Moreover, in these types of filter cavities, Glauber coherent states will deterministically evolve into Schrodinger cat states of a desired order. We discuss potential realizations in quantum nonlinear optics. More broadly, we expect that combining the techniques introduced here with additional "phase-sensitive" nonlinearities (such as second-order nonlinearity) should enable passive stabilization and generation of a wider variety of states than shown here.
Abstract Cat states, as an important resource in the study of macroscopic quantum superposition and quantum information applications, have garnered widespread attention. To date, preparing large-sized optical cat states has remained challenging. We demonstrate that, by utilizing interaction-free measurement and the quantum Zeno effect, even a fragile quantum microscopic system can deterministically control and become entangled with strong light fields, thereby generating large-amplitude optical cat states. During the entire preparation process, our method ensures that the microscopic system functions within a weak field environment, so that its quantum property can be protected. Furthermore, we show that the preparation of cat states is possible even when the quantum microsystem suffers from significant photon loss, provided that optical losses from classical devices are kept low, which implies that the fidelity of the cat state can be enhanced by improvements to and the perfection of the classical optical system.
Large-amplitude squeezed cat states and high-quality Gottesman-Kitaev-Preskill (GKP) states are essential for effective quantum error correction, yet their optical preparation has been hindered by challenges such as low success probabilities, small amplitudes, and insufficient squeezing. Addressing these limitations, our research introduces scalable optical schemes for the deterministic preparation of large-amplitude squeezed cat states from photon-number states. Fock states have the benefit of producing consistent cat states across all measurement outcomes and intrinsically provides a degree of squeezing. Notably, these squeezed cat states facilitate the deterministic generation of high-quality approximate GKP states via "breeding," showing that GKP error correction in optics is technically feasible in near-term experiments. Our schemes allow fault-tolerant quantum computation through the use of GKP error correction.
Abstract Generation of nonclassical states is a necessary requirement for all quantum science and technology protocols. In this regard, Schrödinger cat states, as quantum superpositions of mocroscopically distinguishable coherent states with equal amplitude and opposite phases, have been of great importance in recent years. In this paper, using some appropriate nonlinear optical media, a theoretical scheme is employed to generate various classes of cat-like states with the help of the connection between quantum and nonlinear optics. In fact, we have exploited a single simple method to produce even, odd and also Yurke-Stoler cat-like states by considering different input states such as coherent squeezed, squeezed coherent, photon-added coherent, pair coherent and trio coherent states. To achieve the purpose, we extensively use cross-Kerr interaction and its further generalizations to higher-orders. Projective measurement is the original conception behind the represented approach by which distinct types of nonclassical states are obtained. At last, we pay our attention to the unavoidable effect of field dissipation and show that in most of the above-studied states we may still achieve the cat-like states, however, with attenuated amplitudes.
The Gottesman-Kitaev-Preskill encoding has emerged as a leading candidate for fault-tolerant quantum computation with continuous variables. For photonic architectures, the major challenge is preparing high-quality resource states, which can be deterministically synthesised from many large-amplitude cat states. Thus far, only modest-sized optical cat states have been prepared experimentally, and the implemented methods are highly probabilistic. We propose an all-optical scheme utilising quantum non-demolition interactions and photon-number measurements to prepare large-amplitude cat states with near-unity probability. Importantly, no particular photon-number outcome is postselected: all outcomes contribute to the accumulated photon number, with the protocol repeated until a required threshold is reached. We demonstrate that the scheme is robust to realistic levels of photon-loss, the dominant source of error in optical systems. Our results highlight the power of active Gaussian operations for state preparation and pave the way for efficient quantum error correction using bosonic codes.