Coherence of quantum non-Gaussian states via nonlinear absorption of quanta

TL;DR

The paper tackles generating coherent quantum non-Gaussian states in oscillators where prior linear, phase-insensitive absorption by a ground-state qubit yields non-Gaussianity without local oscillator coherence. It demonstrates that adding a nonlinear phase-insensitive absorption to the linear one creates a mutually active transformation that breaks strict energy-conservation constraints, enabling oscillator coherence. Analyzing both a short-time sequential scheme and a long-time autonomous scheme for k=1 and k=2 couplings, the authors show Wigner-function asymmetry, substantial off-diagonal coherence, and a Fock-space spread extending up to $n\approx7$, with coherence persisting beyond Gaussian-displacement/squeezing corrections. The results remain robust under reasonable dephasing and even with classical initial states, and the authors discuss extensions to oscillator absorbers and reservoir-engineering perspectives, highlighting the broader applicability of drive-free routes to coherent non-Gaussian states in quantum technologies.

Abstract

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.

Figures (15)

• Figure 1: Coherence of quantum non-Gaussian states via a combination of linear and nonlinear absorption by a single qubit: A ground state qubit absorbing fixed quanta of energy (one or two in this illustration) from an oscillator prepared in a Fock state produces only mixtures of Fock states. These states are rotationally symmetric in phase space and therefore the coherence strictly vanishes. In contrast, if both interactions are simultaneous then a superposition of absorptions results which begins to break the rotational symmetry, indicating the emergence of quantum coherence. Wigner function transformations: The transformation of the Wigner function of Fock state $\ket{2}$ remains an incoherent mixture of Fock states for the individual interactions. The combination however results in the emergence of coherence, $\mathcal{C}=0.08$ and the loss of rotational symmetry. The Wigner function in the figure is found for interaction strengths $\frac{g^{(2)}}{g^{(1)}}=0.1$ and short interaction time $\tau=0.157$.
• Figure 2: Sequential emergence of coherent quantum non-Gaussian states, $\mathcal{C}=0.7$ by two sequential linear and nonlinear absorptive operations. The first step, linear absorption, prepares entanglement between qubit and the oscillator but fails to produce coherence in the oscillator (see Wigner function). After the second step with a nonlinear absorption coherence already emerges and the rotational symmetry is strongly broken for higher Fock occupations. The initial state is the Fock state $\ket{7}$, the interaction time is $t=1.57$, the same for both steps, and the remaining detailed parameters are given in Fig. \ref{['BigFig']}.
• Figure 3: The emergence of coherent quantum non-Gaussian states from frequency frustrated nonlinear absorption, stimulated by initially incoherent Fock states in $b$ at a fixed coupling ratio $\frac{g^{(2)}}{g^{(1)}}=0.1$. The initial ($\tau=0$) highly non-Gaussian state is the Fock state $\ket{7}$. The rightmost state corresponds to the maximum coherence, $C\approx4$, achieved over the interval $0\le\tau\le2\pi$ at time $\tau=3.32$ and more than 4 times larger than the short time approximation discussed in the main text. The central states correspond to an example of a state with half the maximum coherence, in this case achieved at $\tau=0.95$. The states remain radically non-Gaussian, containing many negative regions and rotational symmetry is completely lost. The corresponding density matrices, with entries $\rho_{nm}$, below the Wigner functions show that $V$ tends to generate states with superpositions between large and small Fock states with entries very far from the original Fock state, and only small contributions from the ground state. More details on the parameter choices are given in the Appendix.
• Figure 4: The spread into the Fock basis and frustration of energy conservation is captured by the rise in mean energy of the system $\braket{N}$, accompanied by a large increase in the standard deviation $\Delta N$. The maximum coherence occurs at the dashed vertical line. The bar chart shows the maximum coherence generated with $\frac{g^{(2)}}{g^{(1)}}=0.1$ over the range $0\le\tau\le2\pi$ as a function of the initial Fock state $\ket{n}$. The maximum coherence generally increases with $n$ up to saturation at $n=7$. The blue bars indicate the removal of the Gaussian shell via displacement and squeezing operations (detailed in text). The coherence persists and is thus well beyond the covariance matrix approximation.
• Figure 5: An example of the Hamiltonian switching process using $V^{(2)}$ to initiate the qubit-oscillator entanglement. Each interaction has the same time interval $t$, the initial oscillator occupation is $n=7$ and the ratio of coupling strengths is again $\frac{g^{(2)}}{g^{(1)}}=0.1$.