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arXiv:2111.03099

Complete condensation of photon noise in nonlinear dissipative systems

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

Published Nov 4, 2021• 2 citations
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Abstract

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 ($>10^{12}$ photons) with nearly 95% less noise than the standard quantum limit.

DOI
10.48550/arxiv.2111.03099

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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.
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.
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.
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.
It is generally difficult to study the dynamical properties of a quantum system with both inherent quantum noises and nonperturbative nonlinearity. Due to the possibly drastic intensity increase of an input coherent light in gain-loss waveguide couplers with parity-time (PT)(\mathcal{PT})(PT) symmetry, the Kerr effect from a nonlinearity added into the system can be greatly enhanced and is expected to create macroscopic entangled states of the output light fields with huge photon numbers. Meanwhile, quantum noises also coexist with the amplification and dissipation of the light fields. Under the interplay between the quantum noises and nonlinearity, the quantum dynamical behaviors of the systems become rather complicated. However, the important quantum noise effects have been mostly neglected in previous studies about nonlinear PT\mathcal{PT}PT-symmetric systems. Here we present a solution to this nonperturbative quantum nonlinear problem, showing the real-time evolution of the system observables. The enhanced Kerr nonlinearity is found to give rise to a previously unknown decoherence effect that is irrelevant to the quantum noises and imposes a limit on the emergence of macroscopic nonclassicality. In contrast to what happens in linear systems, the quantum noises exert significant impact on the system dynamics and can create nonclassical light field states in conjunction with the enhanced Kerr nonlinearity. This study on the noise involved in quantum nonlinear dynamics of coupled gain-loss waveguides can help to better understand the quantum noise effects in many nonlinear systems.