Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSuperpositions of SU(3) coherent states via a nonlinear evolution
140
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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 explore squeezed coherent states of a 3-dimensional generalized isotonic oscillator whose radial part is the newly introduced generalized isotonic oscillator whose bound state solutions have been shown to admit the recently discovered $X_1$-Laguerre polynomials. We construct a complete set of squeezed coherent states of this oscillator by exploring the squeezed coherent states of the radial part and combining the latter with the squeezed coherent states of the angular part. We also prove that the three mode squeezed coherent states resolve the identity operator. We evaluate Mandels $Q$-parameter of the obtained states and demonstrate that these states exhibit sub-Possionian and super-Possionian photon statistics. Further, we illustrate the squeezing properties of these states, both in the radial and angular parts, by choosing appropriate observables in the respective parts. We also evaluate Wigner function of these three mode squeezed coherent states and demonstrate squeezing property explicitly.
Nonlinear fermions of degree $n$ ($n$-fermions) are introduced as particles with creation and annihilation operators obeying the simple nonlinear anticommutation relation $AA^dagger + {A^dagger}^n A^n = 1$. The ($n+1$)-order nilpotency of these operators follows from the existence of unique $A$-vacuum. Supposing appropreate ($n+1$)-order nilpotent para-Grassmann variables and integration rules the sets of $n$-fermion number states, right and left ladder operator coherent states (CS) and displacement-operator-like CS are constructed. The $(n+1)times(n+1)$ matrix realization of the related para-Grassmann algebra is provided. General $(n+1)$-order nilpotent ladder operators of finite dimensional systems are expressed as polynomials in terms of $n$-fermion operators. Overcomplete sets of (normalized) right and left eigenstates of such general ladder operators are constructed and their properties briefly discussed.
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.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
