Non-Gaussian state preparation and enhancement using weak-value amplification

Abstract

We introduce a protocol for generating a broad class of non-Gaussian (nG) quantum states via postselected weak measurement techniques. The scheme involves injecting an arbitrary quantum state and a single photon into the signal and idler ports, respectively, of an interference setup that incorporates a third-order nonlinear medium. A nG state is conditionally produced at the signal output, heralded by the detection of a single photon in one of the idler output channels. The protocol exploits a weak cross-Kerr interaction and effective single-photon nonlinearity enhanced by the weak-value amplification. We show that by tuning the weak value of the photon number operator in the idler mode within experimentally feasible parameters, a wide variety of nG states can be generated with high fidelity. As specific examples, we demonstrate the generation of photon-added states, displaced and squeezed number states, and a continuum of intermediate nG states using coherent and squeezed vacuum inputs, respectively. Furthermore, we show that the protocol enables the enhancement of non-Gaussianity and the enlargement of Schrödinger cat (SC) states when ideal SC states are used as the input. Our results provide an alternative route for the conditional generation of tunable nG states, with potential applications in quantum information processing. This approach may also open new avenues for quantum state engineering using postselected weak measurements.

Figures (11)

• Figure 1: Schematic of the nG state generation protocol. In this scheme, a given state is prepared in the input signal mode, and a single-photon state is prepared in the idler mode, both of which pass through a MZI. Preselection is performed by sending the single photon through an unbalanced BS with a small deviation $\epsilon$ from the ideal angle $\pi/4$. The signal and idler modes are then coupled via a Kerr medium. A single-photon detection event at one of the idler output ports (i.e., a click at detector $D_{1}$) heralds the desired output state in the output signal mode.
• Figure 2: Fidelity between the generated output state and reference states. Fidelity functions between the signal output state $\vert\Phi^{\prime}\rangle$ and the ideal SPAC state (solid curve), as well as the coherent state $\vert\phi\rangle$ (dashed curve). Here, $\epsilon=0.001$ and $g=0.01$.
• Figure 3: Wigner function of the output state of the generated signal$\vert\Phi^{\prime}\rangle$. a$\beta=0$; b$\beta=0.5$; c$\beta=1$. Other parameters are the same as those used in Fig. \ref{['fig:2']}.
• Figure 4: Second-order correlation function $g^{(2)}(0)$. The blue solid curve corresponds to the generated signal output state $\vert\Phi^{\prime}\rangle$, while the red and green dashed curves represent the coherent state and ideal SPAC state, respectively. Other parameters are the same as those used in Fig. \ref{['fig:2']}.
• Figure 5: Wigner functions (contour plots) and quadrature distributions for the generated state $\vert\Psi\rangle$.a and c show the Wigner functions of the signal input SV states with squeezing parameters $r=-0.7$ and $r=0.2$, respectively. The corresponding Wigner functions of the output signal states $\vert\Psi\rangle$ are shown in b and d. Other parameters are the same as those used in Fig. \ref{['fig:2']}.