Unconditional Preparation of Squeezed Vacuum from Rabi Interactions

Squeezed states of harmonic oscillators are a central resource for continuous-variable quantum sensing, computation, and communication. Here, we propose a method for the generation of very good approximations to highly squeezed vacuum states with low excess antisqueezing using only a few oscillator-qubit coupling gates through a Rabi-type interaction Hamiltonian. This interaction can be implemented with several different methods, which has previously been demonstrated in superconducting circuit and trapped-ion platforms. The protocol is compatible with other protocols manipulating quantum harmonic oscillators, thus facilitating scalable continuous-variable fault-tolerant quantum computation.

Figure 1

(a) Circuit diagram for the generation of a $P$-squeezed vacuum state. The protocol consists of $N$ steps of interactions through the Hamiltonians $\widehat{P}{\widehat{\sigma }}_x$ and $\widehat{X}{\widehat{\sigma }}_y$. The interaction parameters $u_k$ and $v_k$ vary from step to step and are found numerically to optimize the protocol. The protocol is deterministic, but the performance can be slightly improved by measuring the qubit and postselecting on the outcome 0. (b) Evolution of the quadrature distributions during each step of the protocol. Dashed lines correspond to interaction parameters given by Eq. (3) with $L=0.45$ and solid lines correspond to numerically optimized interaction parameters. Note that the negative squeezing value in dB here denotes antisqueezing.

Figure 2

Resulting squeezing as a function of the number of steps of the protocol. For each step, the squeezing increases with $\sim 3–4\mathrm{dB}$. The dashed curve corresponds to adding the optional measurement in Fig. 1 and postselecting on the outcome $|0⟩$, which occurs with high probability.

Figure 3

Obtainable squeezing as a function of noise rate for different noise sources. For each noise source and noise rate, there exists an optimal number of steps. Postselecting on the outcome $|0⟩$ can in some case improve the performance by more than 2 dB.