Related papers: Engineering $\mathrm{SU}(1,1) \otimes \mathrm{SU}(…
For a time-dependent harmonic oscillator with an inverse squared singular term, we find the generalized invariant using the Lie algebra of $SU(2)$ and construct the number-type eigenstates and the coherent states using the…
The U(1,1) and U(2) transformations realized by three-mode interaction in the respective parametric approximations are studied in conditional measurement, and the corresponding non-unitary transformation operators are derived. As an…
We study in this paper the time evolution of $PT$-symmetric non-Hermitian Hamiltonian consisting of periodically driven $SU(1,1)$ generators. A non-Hermitian invariant operator is adopted to solve the Schr\"{o}dinger equation, since the…
Active interferometers use amplifying elements for beam splitting and recombination. We experimentally implement such a device by using spin exchange in a Bose-Einstein condensate. The two interferometry modes are initially empty spin…
We propose a general approach to construct symmetry protected topological (SPT) states i.e the short-range entangled states with symmetry) in 2D spin/boson systems on lattice. In our approach, we fractionalize spins/bosons into different…
This thesis presents an efficient quantum algorithm and explicit circuits for generating eigenstates of arbitrary SU(2) and SU(3) representations. These include a wide variety of highly entangled states. The algorithm uses Schur transform…
We study the Dunkl oscillator in two dimensions by the $su(1,1)$ algebraic method. We apply the Schr\"odinger factorization to the radial Hamiltonian of the Dunkl oscillator to find the $su(1,1)$ Lie algebra generators. The energy spectrum…
A robust scheme for state preparation and state trapping for the spins of two electrons in a semiconductor double quantum dot is presented. The system is modeled by two spins coupled to two independent bosonic reservoirs. Decoherence…
Squeezing a quantum state along a specific direction has long been recognized as a crucial technique for enhancing the precision of quantum metrology by reducing parameter uncertainty. However, practical quantum metrology often involves the…
We suggest a general scheme for quantum state engineering based on conditional measurements carried out on entangled twin-beam of radiation. Realistic detection schemes such as {\sc on/off} photodetection, homodyne detection and joint…
Two-mode squeezed states, which are entangled states with bipartite quantum correlations in continuous-variable systems, are crucial in quantum information processing and metrology. Recently, continuous-variable quantum computing with the…
We report the first experimental demonstration of conditional preparation of a non classical state of light in the continuous variable regime. Starting from a non degenerate OPO which generates above threshold quantum intensity correlated…
We investigate the squeezed regions in the phase plane for non-dissipative dynamical systems controlled by SU(1,1) Lie algebra. We analyze such study for the two SU(1,1) generalized coherent states, namely, the Perelomov coherent state…
Artificial classical wave systems such as wave crystals and metamaterials have demonstrated promising capabilities in simulating a wide range of quantum mechanical phenomena. Yet some gaps between quantum and classical worlds are generally…
We demonstrate coherent manipulation of the nuclear degrees of freedom of ultracold ground-state strontium 87 atoms, thus providing a toolkit for fully exploiting the corresponding large Hilbert space as a quantum resource and for quantum…
SU(1,1) interferometry, proposed in a classic 1986 paper by Yurke, McCall, and Klauder [Phys. Rev. A 33, 4033 (1986)], involves squeezing, displacing, and then unsqueezing two bosonic modes. It has, over the past decade, been implemented in…
We present a characterization of the Hamiltonians that generate optimal-speed unitary time evolution and the associated dynamical trajectory, where the initial states are either pure states or quasi-pure quantum states. We construct the…
We show how entangled qubits can be encoded as entangled coherent states of two-dimensional centre-of-mass vibrational motion for two ions in an ion trap. The entangled qubit state is equivalent to the canonical Bell state, and we introduce…
The robust generation of quantum states in the presence of decoherence is a primary challenge for explorations of quantum mechanics at larger scales. Using the mechanical motion of a single trapped ion, we utilize reservoir engineering to…
We propose a scheme to generate a superposition with arbitrary coefficients on a line in phase space for the center-of-mass vibrational mode of N ions by means of isolating all other spectator vibrational modes from the center-of-mass mode.…