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Register a new userHeralded orthogonalisation of coherent states and their conversion to discrete-variable superpositions
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The nonorthogonality of coherent states is a fundamental property which prevents them from being perfectly and deterministically discriminated. To circumvent this problem, we present an experimentally feasible protocol for the probabilistic orthogonalisation of a pair of coherent states, independent of their amplitude and phase. In contrast to unambiguous state discrimination, successful operation of our protocol is heralded without measuring the states, such that they remain suitable for further manipulation. As such, the resulting orthogonalised state may be used for further processing. Indeed, these states are close approximations of the discrete-variable superposition state $frac{1}{sqrt{2}}left(|0rangle pm |1rangleright)$. This feature, coupled with the non-destructive nature of the operation, is especially useful when considering superpositions of coherent states: such states are mapped to the (weakly squeezed) vacuum or single photon Fock state, depending on the phase of the superposition. Thus this operation may find utility in hybrid continuous-discrete quantum information processing protocols.
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Based on N different coherent states with equal weights and phase-space rotation symmetry, we introduce N-headed incoherent superposition states (NHICSSs) and N-headed coherent superposition states (NHCSSs). These N coherent states are associated with N-order roots of the same complex number. We study and compare properties of NHICSSs and NHCSSs, including average photon number, Mandel Q parameter, quadrature squeezing, Fock matrix elements and Wigner function. Among all these states, only 2HCSS (i.e., Schrodinger cat state) presents quadrature-squeezing effect. Our theoretical results can be used as a reference for researchers in this field.
We consider the optimal approximation of certain quantum states of a harmonic oscillator with the superposition of a finite number of coherent states in phase space placed either on an ellipse or on a certain lattice. These scenarios are currently experimentally feasible. The parameters of the ellipse and the lattice and the coefficients of the constituent coherent states are optimized numerically, via a genetic algorithm, in order to obtain the best approximation. It is found that for certain quantum states the obtained approximation is better than the ones known from the literature thus far.
We show that a nonlinear Hamiltonian evolution can transform an SU(3) coherent state into a superposition of distinct SU(3) coherent states, with a superposition of two SU(2) coherent states presented as a special case. A phase space representation is depicted by projecting the multi-dimensional $Q$-symbol for the state to a spherical subdomain of the coset space. We discuss realizations of this nonlinear evolution in the contexts of nonlinear optics and Bose--Einstein condensates.
We investigate the presence of spin- and planar- squeezing in generalized superpositions of atomic (or spin) coherent states (ACS). Spin-squeezing has been shown to be a useful tool in determining the presence of entanglement in multipartite systems, such as collections of two-level atoms, as well as being an indication of reduced projection noise and sub-shot-noise limited phase uncertainty in Ramsey spectroscopy, suitable for measuring phases $phisim 0$. On the other hand, planar-squeezed states display reduced projection noise in two directions simultaneously and have been shown to lead to enhanced metrological precision in measuring phases without the need for explicit prior knowledge of the phase value. In this paper, we show that the generalized superposition state can be parametrized to display both spin-squeezing along all orthogonal axes and planar-squeezing along all orthogonal planes for all values of $J>1/2$. We close with an application of the maximally spin- and planar-squeezed states to quantum metrology.
We present the generation of approximated coherent state superpositions - referred to as Schrodinger cat states - by the process of subtracting single photons from picosecond pulsed squeezed states of light at 830 nm. The squeezed vacuum states are produced by spontaneous parametric down-conversion (SPDC) in a periodically poled KTiOPO4 crystal while the single photons are probabilistically subtracted using a beamsplitter and a single photon detector. The resulting states are fully characterized with time-resolved homodyne quantum state tomography. Varying the pump power of the SPDC, we generated different states which exhibit non-Gaussian behavior.
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