Entanglement of bosonic modes of material oscillators is studied in the context of two bilinearly coupled, nonlinear oscillators. These oscillators are realizable in the vibrational-cum-bending motions of C-H bonds in dihalomethanes. The bilinear coupling gives rise to invariant subspaces in the Hilbert space of the two oscillators. The number of separable states in any invariant subspace is one more than the dimension of the space. The dynamics of the oscillators when the initial state belongs to an invariant subspace is studied. In particular, the dynamics of the system when the initial state is such that the total energy is concentrated in one of the modes is studied and compared with the evolution of the system when the initial state is such wherein the modes share the total energy. The dynamics of quantities such as entropy, mean of number of quanta in the two modes and variances in the quadratures of the two modes are studied. Possibility of generating maximally entangled states is indicated.
We assess whether a confined Wigner molecule constituted by $2N$ fermions behaves as $N$ bosons or $2N$ fermions. Following the work by C. K. Law [Phys. Rev. A \textbf{71}, 034306 (2005)] and Chudzicki et al. [Phys. Rev. Lett. \textbf{104}, 070402 (2010)] we discuss the physical meaning and the reason why a large amount of entanglement is needed in order to ensure a bosonic composite behavior. By applying a composite boson ansatz, we found that a Wigner molecule confined in two dimensional traps presents a bosonic behavior induced by symmetry. The two-particle Wigner molecule ground state requ…
We reveal the existence of polarizing quantum phases for the enantiomers of cold, interacting chiral molecules in an optical helicity lattice by means of an extended Bose-Hubbard model. These recently proposed lattices have sites with alternating helicity which exert a discriminatory force on chiral molecules with different handedness. In our study of the phase diagram we find that a strong dipolar repulsion between molecules results in the separation of left and right enantiomers.
We consider a simple quantum model of atom-molecule conversion where bosonic atoms can combine into diatomic molecules and vice versa. The many-particle system can be expressed in terms of the generators a deformed $SU(2)$ algebra, and the mean-field dynamics takes place on a deformed version of the Bloch sphere, a teardrop shaped surface with a cusp singularity. We analyse the mean-field and many-particle correspondence, which shows typical features of quantum-classical correspondence. We demonstrate that semiclassical methods can be employed to recover full many-particle features from the me…
We demonstrate a generally applicable technique for mixing two-species quantum degenerate bosonic samples in the presence of an optical lattice, and we employ it to produce low-entropy samples of ultracold 87Rb133Cs Feshbach molecules with a lattice filling fraction exceeding 30%. Starting from two spatially separated Bose-Einstein condensates of Rb and Cs atoms, Rb-Cs atom pairs are efficiently produced by using the superfluid-to-Mott insulator quantum phase transition twice, first for the Cs sample, then for the Rb sample, after nulling the Rb-Cs interaction at a Feshbach resonance's zero cr…
We study ground states and elementary excitations of a system of bosonic atoms and diatomic Feshbach molecules trapped in a one-dimensional optical lattice using exact diagonalization and variational Monte Carlo methods. We primarily study the case of an average filling of one boson per site. In agreement with bosonization theory, we show that the ground state of the system in the thermodynamic limit corresponds to the Pfaffian-like state when the system is tuned towards the superfluid-to-Mott insulator quantum phase transition. Our study clarifies the possibility of the creation of exotic Pfa…
Bosonic quantum conversion systems can be modeled by many-particle single-mode Hamiltonians describing a conversion of $n$ molecules of type A into $m$ molecules of type B and vice versa. These Hamiltonians are analyzed in terms of generators of a polynomially deformed $su(2)$ algebra. In the mean-field limit of large particle numbers, these systems become classical and their Hamiltonian dynamics can again be described by polynomial deformations of a Lie algebra, where quantum commutators are replaced by Poisson brackets. The Casimir operator restricts the motion to Kummer shapes, deformed Blo…
We, based on the photoassociation of fermion atoms into bosonic molecules, propose a scheme to create the steady entanglement between the atom state and the molecule state inside an optical lattice. The stability of entanglement state is guaranteed by sweeping the frequency of Ramman laser beam through resonance according to the second Demkov-Kunike (DK2) nonadiabatic transition model\cite{DK,models}. The probability amplitude of each components can be precisely controlled by adjusting the sweeping parameter.
QuTiP-BoFiN: A bosonic and fermionic numerical hierarchical-equations-of-motion library with applications in light-harvesting, quantum control, and single-molecule electronics
We model collisionless collective conversion of a degenerate Fermi gas into bosonic molecules via a Feshbach resonance, treating the bosonic molecules as a classical field and seeding the pairing amplitudes with random phases. A dynamical instability of the Fermi sea against association into molecules initiates the conversion. The model qualitatively reproduces several experimental observations {[Regal et al., Nature {\bf 424}, 47 (2003)]}. We predict that the initial temperature of the Fermi gas sets the limit for the efficiency of atom-molecule conversion.
Time-evolution of the vibrational states of two interacting harmonic oscillators in the local mode scheme is presented. A local-to-normal mode transition (LNT) is identified and studied from the time dependent point of view. The LNT is established as a polyad breaking phenomenon from the local point of view for the stretching degrees of freedom in a triatomic molecule. This study is carried out in the algebraic representation of bosonic operators. The dynamics of the states are determined via the solutions of the corresponding nonlinear Ermakov equation. Application of this formalism to H$_2$O…
It is shown that fermionic polar molecules or atoms in a bilayer optical lattice can undergo the transition to a state with circulating currents, which spontaneously breaks the time reversal symmetry. Estimates of relevant temperature scales are given and experimental signatures of the circulating current phase are identified. Related phenomena in bosonic and spin systems with ring exchange are discussed.
We study the ground state and the thermal phase diagram of a two-species Bose-Hubbard model, with $U(1)\times \mathbb{Z}_2$ symmetry, describing atoms and molecules on a 2D optical lattice interacting via a Feshbach resonance. Using quantum Monte Carlo simulations and mean field theory, we show that the conversion between the two-species, coherently coupling the atomic and molecular states, has a crucial impact on the Mott-Superfluid transition and stabilizes an insulating phase with a gap controlled by the conversion term -- \textit{the Feshbach insulator} -- instead of a standard Mott insula…
An even number of fermions can behave in a bosonic way. The simplest scenario involves two fermions which can form a single boson. But four fermions can either behave as two bipartite bosons or further assemble into a single four-partite bosonic molecule. In general, for 2N fermions there are many possible arrangements into composite bosons. The question is: what determines which fermionic arrangement is going to be realized in a given situation and can such arrangement be considered truly bosonic? This work aims to find the answer to the above question. We propose an entanglement-based method…
We study hybrid atom-molecule quantum walks in one-dimensional optical lattices with two interacting bosonic atoms which may be converted into a molecule. The hybrid atom-molecule energy bands include a continuum band and two isolated bands, which respectively correspond to scattering states and dressed bound states (DBS's). Because of the atom-molecule coupling, the DBS's may appear even in the absence of atom-atom interaction. From an initial state of two atoms occupying the same site, in addition to independent quantum walks which correspond to scattering states, correlated quantum walks ap…
We adopt a three-level bosonic model to investigate the quantum phase transition in an ultracold atom-molecule conversion system which includes one atomic mode and two molecular modes. Through thoroughly exploring the properties of energy level structure, fidelity, and adiabatical geometric phase, we confirm that the system exists a second-order phase transition from an atommolecule mixture phase to a pure molecule phase. We give the explicit expression of the critical point and obtain two scaling laws to characterize this transition. In particular we find that both the critical exponents and …
We study the quantum phase transitions of a model that describes the interconversion of interacting bosonic atoms and molecules. Using a classical analysis, we identify a threshold coupling line separating a molecular phase and a mixed phase. Through studies of the energy gap, von Neumann entanglement entropy, and fidelity, we give evidence that this line is associated to a boundary line in the ground-state phase diagram of the quantum system.
Bound structures among dipolar molecules in multilayers are a topic of great interest in the light of recent experiments that have demonstrated the feasibility of the setup. While it is known that two molecules in two adjacent layers will always bind, larger complexes have only been scarcely addressed thus far. Here we prove rigorously that three- and four-body states will never be bound when the dipoles are oriented perpendicular to the layers. The technique employed is general and can be used for more molecules/layers and other geometries. Our analytical findings are supported by numerical c…
Quantum error correction beyond $SU(2)$: spin, bosonic, and permutation-invariant codes from convex geometry
University of Maryland, College Park（马里兰大学帕克分校）；Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park（美国国家标准与技术研究院/马里兰大学联合量子信息与计算科学中心）
Ultracold polar molecules provide an excellent platform to study quantum many-body spin dynamics, which has become accessible in the recently realized low entropy quantum gas of polar molecules in an optical lattice. To obtain a detailed understanding for the molecular formation process in the lattice, we prepare a density distribution where lattice sites are either empty or occupied by a doublon composed of a bosonic atom interacting with a fermionic atom. By letting this disordered, out-of-equilibrium system evolve from a well-defined initial condition, we observe clear effects on pairing th…
