Related papers: Transformation design and nonlinear Hamiltonians
Reduced abstract. This Thesis explores emergent cooperative phenomena in collective light-matter systems. We study ensembles of interacting quantum emitters coherently driven by a laser field and coupled to photonic structures, focusing on…
The Heisenberg picture for non-Hermitian but $\eta$-pseudo-Hermitian Hamiltonian systems is suggested. If a non-Hermitian but $\eta$-pseudo-Hermitian Hamiltonian leads to real second order equations of motion, though their first order…
We consider hamiltonian models representing an arbitrary number of spin $1/2$ fermion quantum fields interacting through arbitrary processes of creation or annihilation of particles. The fields may be massive or massless. The interaction…
A quantum state for being an eigenstate of some local Hamiltonian should be constraint by zero energy variance and consequently, the constraint is rather strong that a single eigenstate may uniquely determine the Hamiltonian. For…
We construct a new class of non-Hermitian Hamiltonians with real spectra. The Hamiltonians possess one explicitly known eigenfunction.
We use the dynamical algebra of a quantum system and its dynamical invariants to inverse engineer feasible Hamiltonians for implementing shortcuts to adiabaticity. These are speeded up processes that end up with the same populations than…
The celebrated quantum no-cloning theorem states that an arbitrary quantum state cannot be cloned perfectly. This raises questions about cloning of classical states, which have also attracted attention. Here, we present a physical approach…
Generating large, non-trivial quantum chemistry test problems with known ground-state solutions remains a core challenge for benchmarking electronic structure methods. Inspired by planted-solution techniques from combinatorial optimization,…
In the holonomic approach to quantum computation information is encoded in a degenerate eigenspace of a parametric family of Hamiltonians and manipulated by the associated holonomic gates. These are realized in terms of the non-abelian…
We propose to synthesize arbitrary nonclassical motional states in optomechanical systems by using sideband excitations and photon blockade. We first demonstrate that the Hamiltonian of the optomechanical systems can be reduced, in the…
The manipulation of the quantum states of light in linear optical systems has multiple applications in quantum optics and quantum computation. The package QOptCraft gives a collection of methods to solve some of the most usual problems when…
Recently, the search for topological states of matter has turned to non-Hermitian systems, which exhibit a rich variety of unique properties without Hermitian counterparts. Lattices modeled through non-Hermitian Hamiltonians appear in the…
We construct an effective Hamiltonian of interacting bosons, based on scattered radiation off vibrational modes of designed molecular architectures. Making use of the infinite yet countable set of spatial modes representing the scattering…
We study the quantum properties of light propagating through an array of coupled nonlinear waveguides and forming a discrete soliton. We demonstrate that it is possible to use certain types of quasi-solitons to form continuous variables…
We study a motion of quantum particles, whose properties depend on one coordinate so that they can move freely in the perpendicular direction. A rotationally-symmetric Hamiltonian is derived and applied to study a general interface formed…
The entanglement Hamiltonian $H_E$, defined through the reduced density matrix of a subsystem $\rho_A=\exp(-H_E)$, is an important concept in understanding the nature of quantum entanglement in many-body systems and quantum field theories.…
Modeling non-Hermitian Hamiltonians is increasingly important in classical and quantum domains, especially when studying open systems, $PT$ symmetry, and resonances. However, the quantum simulation of these models has been limited by the…
We investigate how quantum state can be converted between continuous variable and qubits systems. Non-linear Jaynes-Cumings interaction Hamiltonian is introduced to accomplish the conversion. Detail analysis on the conversion of thermal…
The quantum mechanical motion of the atomic nuclei is considered over a single- or a multi-dimensional subspace of electronic states which is separated by a gap from the rest of the electronic spectrum over the relevant range of nuclear…
When canonical Hamiltonians of local quantum field theories are transformed using a renormalization group procedure for effective particles, the resulting interaction terms are non-local. The range of their non-locality depends on the…