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arXiv:2606.30021

Deterministic nonlinear bunching of bosons

Kingshuk Adhikary, Darren W. Moore, Radim Filip

quant-phSubmitted Jun 29, 2026• Announced Jun 30, 2026• 0 citations
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Abstract

The ability of bosonic energy quanta to bunch together in an energy-conserving interaction is a fundamental feature of quantum harmonic oscillators. Linear systems together with measurement allow for the conditional concentration of energy quanta and, subsequently, breeding of the quantum states, but only with an exponentially decreasing success rate. Deterministic, energy-conserving and unconditional bunching however, requires nonlinearity. We investigate which nonlinear energy-conserving interactions deterministically combine bosons into high number states at the same frequency. We show that in order to do so it is advantageous to use nonlinear interactions involving highly saturable systems, such as qubits, as they preserve the hierarchical quantum non-Gaussian features and are also sufficiently robust against pure loss. Nonlinear bunching therefore demonstrates the advantage of a {\it qubit-inside} nonlinearity and opens new directions in the deterministic preparation, processing, and detection of quantum non-Gaussian states.

Comments
8 pages includes references and appendices; 4 + 2 figs

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The ability of bosonic energy quanta to bunch together in an energy-conserving interaction is a fundamental feature of quantum harmonic oscillators. Linear systems together with measurement allow for the conditional concentration of energy quanta and, subsequently, breeding of the quantum states, but only with an exponentially decreasing success rate. Deterministic, energy-conserving and unconditional bunching however, requires nonlinearity. We investigate which nonlinear energy-conserving interactions deterministically combine bosons into high number states at the same frequency. We show that in order to do so it is advantageous to use nonlinear interactions involving highly saturable systems, such as qubits, as they preserve the hierarchical quantum non-Gaussian features and are also sufficiently robust against pure loss. Nonlinear bunching therefore demonstrates the advantage of a {\it qubit-inside} nonlinearity and opens new directions in the deterministic preparation, processing, and detection of quantum non-Gaussian states.
The linear and phase insensitive absorption of a single quanta via coherent interactions with a saturable system, even a single ground state qubit, is sufficient to deterministically generate quantum non-Gaussian states in an oscillator, even stimulated merely by increasing thermal oscillator energy. However, the resultant states only approach Fock states and therefore do not exhibit quantum coherence. Here we overcome this limitation using a minimal step: a nonlinear phase-insensitive absorption process added to the linear one. The coherent addition of such individually passive processes allows coherence to emerge and increase in phase space without an external drive and with minimal interaction requirements. The coherence of quantum non-Gaussian states emerges because the linear and nonlinear absorption processes are not mutually passive. In the simplest case rotationally symmetric Wigner functions of the oscillator Fock states convert their many negative regions to an extremely complex asymmetric structure in sharp contrast to the rotational symmetry of those obtained by the individual interactions. We extend this case to include an unsaturable absorber (oscillator) and analyse switching between linear and nonlinear absorptions, suitable for broad classes of experiments.
Quantum nonlinear operations for harmonic oscillator systems play a key role in the development of analog quantum simulators and computers. Since strong highly nonlinear operations are often unavailable in the existing physical systems, it is a common practice to approximate them by using conditional measurement-induced methods. The conditional approach has several drawbacks, the most severe of which is the exponentially decreasing success rate of the strong and complex nonlinear operations. We show that by using a suitable two level system sequentially interacting with the oscillator, it is possible to resolve these issues and implement a nonlinear operation both nearly deterministically and nearly perfectly. We explicitly demonstrate the approach by constructing self-Kerr and cross-Kerr couplings in a realistic situation, which require a feasible dispersive coupling between the two-level system and the oscillator.
The focus of the study is the free quantum evolution of Duffing oscillators which are nonlinearly coupled to bosonic environments. The work evolves from a particular system of an undamped, nonlinear graphene resonator mode to a more generalized framework of oscillator modes interacting with two different configurations of bosonic environments. In a model with no dissipation, the nonlinear Duffing oscillator allows an initial coherent state to evolve into a macroscopic superposition state, a Schrödinger Cat state. By further subjecting a Duffing mode to nonlinear damping, the parity conservation due to the two-quanta system-bath exchange, brings the system to a nonclassical steady state - an equilibrium state very much different from the ground state. The quantum features of this state are analysed for temperatures above zero and in a more realistic scenario where the interplay of linear and nonlinear decay is taken into account. The scope of the study is then extended to bipartite systems of nonlinear interacting oscillators, each nonlinearly coupled to a bosonic environment. The generation of entanglement in initially separable states and entanglement's asymptotic behaviour are investigated. One of the outcomes is the Duffing nonlinearity not affecting the entanglement asymptote. Therefore, finally a bipartite system of harmonic oscillators, with nonlinear system-bath coupling is initiated with entangled, squeezed states, and the asymptotic behaviour is evaluated in the parameter space of temperature, squeezing and dissipation rate. This is done for common and individual reservoir configurations, and either zero or non-zero inter-mode coupling.
Abstract Maxwell's demon principle of extracting valuable resources through measuring fluctuations in the system already stimulated modern quantum physics. In contrast to classical physics, a free coupling to a probe and its free measurement fundamentally shape the system state. This becomes a new dimension of the Maxwell demon effect, as in addition to the gained information, the back action on the system can be exploited and essential for further applications. We investigate quantum bosonic Maxwell's demon nonlinearly coupled to a two-level system to shift its paradigm to quantum nonlinear physics. The deterministic multiple subtractions of single energy quantum by an energetically conservative Jaynes-Cummings interaction leads to an out-of-equilibrium state. Although still super-Poissonian, it can resonantly excite another two-level system better than any thermal state. Making use of an already available and energetically conserved nonlinear Jaynes-Cummings to absorb multiple bosons, nonlinear subtractions can exclusively suppress the tails of bosonic noise to reach an out-of-equilibrium state whose statistics and mean-to-noise ratio are close to that of Possonian distributions. The improvement becomes significant for successfully exciting hundreds of qubits as including few additional optimal nonlinear subtractions can improve the success rate 10 times higher than the linear scheme.
Bosonic systems with negative Wigner function superposition states are fundamentally witnessing nonlinear quantum dynamics beyond linearized systems and, recently, have become essential resources of quantum technology with many applications. Typically, they appear due to sophisticated combination of external drives, nonlinear control, measurements or strong nonlinear dissipation of subsystems to an environment. Here, we propose a conceptually different and more autonomous way to obtain such states, avoiding these ingredients, using purely sudden interaction decay in the paradigmatic interacting qubit-oscillator system weakly coupled to bath at thermal equilibrium in a low-temperature limit. We demonstrate simultaneously detectable unconditional negative Wigner function and quantum coherence and their qualitative enhancement employing more qubits.
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.