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Macroscopic condensation of photon noise in sharply nonlinear dissipative systems

Nicholas Rivera, Jamison Sloan, Yannick Salamin, Marin Soljacic A

Published Nov 4, 2021• 1 citation
OpenAlex

Abstract

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.

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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.
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=1000n=1000n=1000, while in another, we show how conventional laser architectures could be used to generate macroscopic light (>1012>10^{12}>1012 photons) with nearly 95% less noise than the standard quantum limit.
Nonclassical states of light, such as number-squeezed light, with fluctuations below the classical shot noise level, have important uses in metrology, communication, quantum information processing, and quantum simulation. However, generating these nonclassical states of light, especially with high intensity and a high degree of squeezing, is challenging. To address this problem, we introduce a new concept which uses gain to generate intense sub-Poissonian light at optical frequencies. It exploits a strongly nonlinear gain for photons which arises from a combination of frequency-dependent gain and Kerr nonlinearity. In this laser architecture, the interaction between the gain medium and Kerr nonlinearity suppresses the spontaneous emission at high photon number states, leading to a strong "negative feedback" that suppresses photon-number fluctuations. We discuss realistic implementations of this concept based on the use of solid-state gain media in laser cavities with Kerr nonlinear materials, showing how 90% squeezing of photon number fluctuations below the shot noise level can be realized.
The quantization of the electromagnetic field leads directly to the existence of quantum mechanical states, called Fock states, with an exact integer number of photons. Despite these fundamental states being long-understood, and despite their many potential applications, generating them is largely an open problem. For example, at optical frequencies, it is challenging to deterministically generate Fock states of order two and beyond. Here, we predict the existence of an effect in nonlinear optics, which enables the deterministic generation of large Fock states at arbitrary frequencies. The effect, which we call an n -photon bound state in the continuum, is one in which a photonic resonance (such as a cavity mode) becomes lossless when a precise number of photons n is inside the resonance. Based on analytical theory and numerical simulations, we show that these bound states enable a remarkable phenomenon in which a coherent state of light, when injected into a system supporting this bound state, can spontaneously evolve into a Fock state of a controllable photon number. This effect is also directly applicable for creating (highly) squeezed states of light, whose photon number fluctuations are (far) below the value expected from classical physics (i.e., shot noise). We suggest several examples of systems to experimentally realize the effects predicted here in nonlinear nanophotonic systems, showing examples of generating both optical Fock states with large n ( n > 10), as well as more macroscopic photonic states with very large squeezing, with over 90% less noise (10 dB) than the classical value associated with shot noise.
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.