We present a new type of dissipation unique to nonlinear optical systems. We show how this phenomenon enables a new type of laser that deterministically creates macroscopic Fock states of light at optical frequencies.
Fock states are the most fundamental quantum states of bosonic fields, forming an important basis for understanding their quantum dynamics. As energy and number eigenstates, they have an exactly defined number of quanta, and most faithfully express the particle nature of fields. These properties make them attractive for many applications in metrology, and quantum simulation and information processing. Yet, Fock states are notoriously difficult to generate. The problem is especially acute in optics, where it is difficult to deterministically produce Fock states with more than a single photon, let alone at macroscopic scales. This is in part due to a dearth of mechanisms to produce large Fock states, as well as the deleterious effects of linear dissipation. Here, we introduce a new effect in the physics of nonlinear bosons, arising from the interplay of dissipation and Kerr nonlinearity. In this effect, a nonlinear resonance is dissipationless when it has a particular number of quanta (e.g., photons) inside it, and lossy otherwise. This loss, which results from nonlinear interference, leads to several new quantum statistical effects. For example, it leads to spontaneous condensation of intensity noise, which may enable generation of large Fock and extremely photon-number-squeezed states of light. We also show how this effect has implications for new classes of optoelectronic devices such as lasers, which can stabilize extremely low-noise states in an equilibrium between gain and the nonlinear loss that we introduce. Throughout the text, we present examples of systems that may realize these effects. In one, we show how the nonlinear dissipation could lead to optical Fock states of n=1000, while in another, we show how conventional laser architectures could be used to generate macroscopic light (>1012 photons) with nearly 95% less noise than the standard quantum limit.
Macroscopic non-Gaussian states of light are among the most highly-coveted holy grails in quantum science and technology. An important example is that of macroscopic number (Fock) states of light. Due to their exactly defined number of photons, they are of great interest in quantum metrology, spectroscopy, simulation, and information processing. However, the deterministic creation and stabilization of even approximate large-number Fock states remains thus far a long-standing open problem. Here, we introduce a mechanism that deterministically generates macroscopic sub-Poissonian states, including Fock states, at optical and infrared frequencies. The method takes advantage of the fact that a photon with a sharply increasing nonlinear loss will have its intensity noise condense as it decays. We reveal regimes where this phenomenon can lead to transient generation of Fock and sub-Poissonian states. We further show that these low noise states can be preserved in steady-state by building a laser with a sharp loss element, stabilizing the state with an equilibrium between gain and loss. We show two examples of these phenomena: one which produces a near-Fock state with 5,000 photons (with an uncertainty of 1 photon), and one which generates a macroscopic sub-Poissonian state with over a trillion photons, yet noise 99% below that of a coherent state of the same size. When realized, our results may enable many of the previously envisaged applications of number states and sub-Poissonian states for quantum algorithms, simulation, metrology, and spectroscopy. More generally, our results provide a new and general type of nonlinearity which could form the basis for many new optoelectronic devices which emit macroscopic non-Gaussian light.
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.
The interaction of light and matter can be described by a set of coupled nonlinear evolution equations for the material and electromagnetic fields. In order to account for the effects of vacuum fluctuations, noise forces which cause spontaneous transitions have to be included. In these macroscopic systems various sources of noise besides fundamental quantum fluctuations exist which are of macroscopic origin. These cause fluctuations of the cavity dissipation as well as of the external pumping power. In the course of an adiabatic elimination procedure, these fluctuations appear as multiplicative noise in the equations of motion (e.g. for the field intensity, due to the nonlinearity of the interaction). While fluctuations of the cavity damping create noise linear in the field intensity, randomness in the pump strength causes fluctuations that depend nonlinearly on the light intensity. In this respect, the noise terms enter the equations of motion quite differently and have to be distinguished from spontaneous emission noise which is independent of the field strength, and is the basis of all traditional laser models.