In this work, we investigate the generation of squeezed Schrödinger cat states in schemes based on photon-number-resolving measurements on multimode Gaussian states. We derive analytical expressions for the states generated in two- and three-mode schemes, as well as formulas for their fidelity with squeezed Schrödinger cat states. We analyze how the amplitude of the generated states scales with the number of detected particles. Furthermore, we derive an upper bound on the achievable generation fidelity and identify the conditions under which multimode schemes can enhance the quality of the generated states.
Light is a perfect candidate to carry out quantum information for applications to quantum computation, communication and metrology. Information can be encoded using observables with discrete spectrum (or DV for discrete variable encoding) as well as with continuous spectrum observables (or CV for continuous variable encoding). One of the most used states to encode a CV qubit is the so called optical Schrödinger cat state, i.e. a superposition of two coherent states with the same amplitude and opposite phases. Approximation of these states, named Schrödinger kittens, have been generated in an heralded fashion by subtraction of one or two photons from a degenerate single mode squeezed vacuum states. Experiments have been conducted in continuous wave regime generally using optical parametric oscillators as well as in the pulsed regime. The quality of Schrödinger kittens generated with this strategy, however, suffers from the impurity of the squeezing in the wave-packet of the heralded state. In the CW regime, it is shown theoretically and experimentally that a narrowband filtering of the heralding photon increase the purity of thegenerated state. We extend this study so as to describe also the pulsed regime where the squeezed vacuum state is in general spectrally multimode. We calculate and numerically simulate the state generated when subtracting a photon from an arbitrary multimode pulsed squeezed vacuum state. Inaddition, we investigate its homodyne detection by considering an arbitrary pulsed local oscillator. The fidelity between the heralded state and a perfect single mode photon subtracted squeezed state decreases when the number of modes excited in the multimode squeezed vacuum increases. We show how to increase this fidelity by using a narrowband filter in the heralding path. This study quantifies the effect of spectral filtering on the quality of the generated state using a multimode approach that can be applied to a wide variety of situations. We believe that it will have a major impact on realisation of non-Gaussian states in an heralded fashion.
A cat-state is a superposition of two coherent states with amplitudes
α0 and
−α0. Recent experiments create cat states in a microwave cavity field using superconducting circuits. As with degenerate parametric oscillation (DPO) in an adiabatic and highly nonlinear limit, the states are formed in a signal cavity mode via a two-photon dissipative process induced by the down conversion of a pump field to generate pairs of signal photons. The damping of the signal and the presence of thermal fluctuations rapidly decoheres the state, and the effect on the dynamics is to either destroy the possibility of a cat state, or else to sharply reduce the lifetime and size of the cat-states that can be formed. In this paper, we study the effect on both the DPO and microwave systems of a squeezed reservoir coupled to the cavity. While the threshold nonlinearity is not altered, we show that the use of squeezed states significantly lengthens the lifetime of the cat states. This improves the feasibility of generating cat states of large amplitude and with a greater degree of quantum macroscopic coherence, which is necessary for many quantum technology applications. Using current experimental parameters for the microwave set-up, which requires a modified Hamiltonian, we further demonstrate how squeezed states enhance the quality of the cat states that could be formed in this regime. Squeezing also combats the significant decoherence due to thermal noise, which is relevant for microwave fields at finite temperature. By modeling a thermal squeezed reservoir, we show that the thermal decoherence of the dynamical cat states can be inhibited by a careful control of the squeezing of the reservoir. To signify the quality of the cat state, we consider different signatures including fringes and negativity, and the
Cl1 measure of quantum coherence.