Deterministic Shaping of Quantum Light Statistics

Abstract

We propose a theoretical method for the deterministic shaping of quantum light via photon number state selective interactions. Nonclassical states of light are an essential resource for high precision optical techniques that rely on photon correlations and noise reshaping. Notable techniques include quantum enhanced interferometry, ghost imaging, and generating fault tolerant codes for continuous variable optical quantum computing. We show that a class of nonlinear-optical resonators can transform many-photon wavefunctions to produce structured states of light with nonclassical noise statistics. The devices, based on parametric down conversion, utilize the Kerr effect to tune photon number dependent frequency matching, inducing photon number selective interactions. With a high amplitude coherent pump, the number selective interaction shapes the noise of a two-mode squeezed cavity state with minimal dephasing, illustrated with simulations. We specify the requisite material properties to build the device and highlight the remaining material degrees of freedom which offer flexible material design.

Figures (4)

• Figure 1: General characteristics of NSOPO. In each plot the state is initially a uniform real valued distribution. The plots differ only in the phase of the NSOPO complex squeezing parameters $\Xi$. For all plots, the gouge center $n'=60$, the Kerr detuning $\gamma = \pi$, and the evolution time $\tau = 0.08$. Orange dots are spaced by the predicted peak spacing, $s = \frac{2\pi}{\gamma \tau}$, and aligned with the shaping center. The green curve shows a first order approximation of shaping that follows the peak positions and magnitude closely. The blue curve is the shaped photon probability distribution resulting from an in initial uniform distribution.
• Figure 2: Examples of photon probability shaping offered by NSOPO. (a) An approximate Fock state of $n = 52$ accomplished by placing the shaping center on the peak of an initial coherent state with amplitude $\alpha_{s,i} = 7$. (b) A precision shaping of the same coherent state. Parameter $\gamma t$ is chosen such that peak spacing $s$ is two photons. (c) A two mode squeezed vacuum state with $s = 2$. (d) A two mode squeezed vacuum with $s = 6$.
• Figure 3: (a) Wigner function of an initial coherent state of amplitude $\alpha = 7$. (b) The coherent state subject to Kerr rotation without any NSOPO. (c-f) The state shaped with NSOPO complex squeezing parameter $\pm2, \pm2i$. In all plots, blue regions are positive valued and red regions are negative. Every state is shaped with parameters $\gamma = \pi/2, \tau = 1, n' = 8$. As the phase of $\Xi$ is varied by increments of $\pi/2$, number selective shaping changes predictably.
• Figure 4: Both plots present data from a simulation generating an approximate N=5 Fock state in the presence of incoherent loss. The state is evolved from an initial two mode squeezed coherent state of amplitude $\alpha = 2$. The Hamiltonian parameters are $|\Xi|\tau = .3$, $\gamma \tau = 0.9$ and $n' = 4$. Plot (a) shows the growth of quantum infidelity $1-F$ with respect to reciprocal NSOPO peak spacing $\gamma t = \frac{2\pi}{s}$. Each curve represents a different value of the strength to loss ratio $\gamma/\Gamma_{cav}$ where $\gamma$ is the the adjacent state detuning and $\Gamma_{cav}$ is the decay rate of the cavity at the signal and idler frequencies. Plot (b) shows the effect of loss on corresponding photon number probabilities.