Search results for "QUANTUM MECHANICS"

Dressed emitters as impurities

2021

Dressed states forming when quantum emitters or atoms couple to a photonic bath underpin a number of phenomena and applications, in particular dispersive effective interactions occurring within photonic bandgaps. Here, we present a compact formulation of the resolvent-based theory for calculating atom-photon dressed states built on the idea that the atom behaves as an effective impurity. This establishes an explicit connection with the standard impurity problem in condensed matter. Moreover, it allows us to formulate and settle in a model-independent context a number of properties previously known only for specific models or not entirely formalized. The framework is next extended to the cas…

Quantum localization and bound state formation in Bose-Einstein condensates

2010

We discuss the possibility of exponential quantum localization in systems of ultracold bosonic atoms with repulsive interactions in open optical lattices without disorder. We show that exponential localization occurs in the maximally excited state of the lowest energy band. We establish the conditions under which the presence of the upper energy bands can be neglected, determine the successive stages and the quantum phase boundaries at which localization occurs, and discuss schemes to detect it experimentally by visibility measurements. The discussed mechanism is a particular type of quantum localization that is intuitively understood in terms of the interplay between nonlinearity and a bou…

Compact two-electron wave function for bond dissociation and Van der Waals interactions: A natural amplitude assessment

2014

Electron correlations in molecules can be divided in short range dynamical correlations, long range Van der Waals type interactions and near degeneracy static correlations. In this work we analyze for a one-dimensional model of a two-electron system how these three types of correlations can be incorporated in a simple wave function of restricted functional form consisting of an orbital product multiplied by a single correlation function $f(r_{12})$ depending on the interelectronic distance $r_{12}$. Since the three types of correlations mentioned lead to different signatures in terms of the natural orbital (NO) amplitudes in two-electron systems we make an analysis of the wave function in t…

Long-range interactions and the sign of natural amplitudes in two-electron systems

2013

In singlet two-electron systems the natural occupation numbers of the one-particle reduced density matrix are given as squares of the natural amplitudes which are defined as the expansion coefficients of the two-electron wave function in a natural orbital basis. In this work we relate the sign of the natural amplitudes to the nature of the two-body interaction. We show that long-range Coulomb-type interactions are responsible for the appearance of positive amplitudes and give both analytical and numerical examples that illustrate how the long-distance structure of the wave function affects these amplitudes. We further demonstrate that the amplitudes show an avoided crossing behavior as func…

Coherence and entanglement dynamics of vibrating qubits

2017

We investigate the dynamics of coherence and entanglement of vibrating qubits. Firstly, we consider a single trapped ion qubit inside a perfect cavity and successively we use it to construct a bipartite system made of two of such subsystems, taken identical and noninteracting. As a general result, we find that qubit vibration can lead to prolonging initial coherence in both single-qubit and two-qubit system. However, despite of this coherence preservation, we show that the decay of the entanglement between the two qubits is sped up by the vibrational motion of the qubits. Furthermore, we highlight how the dynamics of photon-phonon correlations between cavity mode and vibrational mode, which…

Unconventional phases of attractive Fermi gases in synthetic Hall ribbons

2017

An innovative way to produce quantum Hall ribbons in a cold atomic system is to use M hyperfine states of atoms in a one-dimensional optical lattice to mimic an additional "synthetic dimension." A notable aspect here is that the SU(M) symmetric interaction between atoms manifests as "infinite ranged" along the synthetic dimension. We study the many-body physics of fermions with SU(M) symmetric attractive interactions in this system using a combination of analytical field theoretic and numerical density-matrix renormalization-group methods. We uncover the rich ground-state phase diagram of the system, including unconventional phases such as squished baryon fluids, shedding light on many-body…

Front propagation in the one-dimensional autocatalyticA+B→2Areaction with decay

1999

We consider front propagation in the autocatalytic scheme $A+\stackrel{\ensuremath{\rightarrow}}{B}2A,$ where we also allow the A particles to decay, $\stackrel{\ensuremath{\rightarrow}}{A}0,$ with a constant decay rate $\ensuremath{\beta}.$ In a one dimensional, discrete, situation the A domain moves as a pulse, and its dynamics differs from what is found in higher dimensions. Thus the velocity of the pulse tends to a finite value when $\ensuremath{\beta}$ approaches from below the critical value ${\ensuremath{\beta}}_{c},$ at which pulses die out. On the other hand, when approaching ${\ensuremath{\beta}}_{c}$ from above, the mean lifetime of the pulse grows as $T\ensuremath{\propto}(\ensu…

Trying to fuse the basic mathematical ideas of quantum TGD to a single coherent whole

The theoretical framework behind TGD involves several different strands and the goal is to unify them to a single coherent whole. TGD involves number theoretic and geometric visions about physics and $M^8-H$ duality, analogous to Langlands duality, is proposed to unify them. Also quantum classical correspondence (QCC) is a central aspect of TGD. One should understand both the $M^8-H$ duality and QCC at the level of detail. The following mathematical notions are expected to be of relevance for this goal. \begin{enumerate} \item Von Neumann algebras, call them $M$, in particular hyperfinite factors of type $II_1$ (HFFs), are in a central role. Both the geometric and number theoretic side, QCC…

Some New Ideas Related to Langlands Program viz. TGD

Langlands' program seeks to relate Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local fields and adeles. Langlands program is described by Edward Frenkel as a kind of grand unified theory of mathematics. In the TGD framework, $M^8-M^4\times CP_2$ duality assigns to a rational polynomial a set of mass shells $H^3$ in $M^4\subset M^8$ and by associativity condition a 4-D surface in $M^8$, and its it to $H=M^4\times CP_2$. $M^8-M^4\times CP_2$ means that number theoretic vision and geometric vision of physics are dual or at least complementary. This vision could extend to a trinity of number theoretic, geometric and topologica…

Bohm’s Implicate Order, Wheeler’s Participatory Universe, Stapp’s Mindful Universe, Zurek’s Quantum Darwinism and the Buddhist Mind-Only Ground Consc…

According to quantum physicist Erich Joos the following three issues are the outstanding quantum conundrums of deep significance: 1. The meaning of the wavefunction; 2. The exact nature of the mechanism of the collapse; 3. The connection between the quantum and classical realm. In this paper I shall attempt to elucidate a possible approach to these central issues by drawing parallels between David Bohm’s notion of the implicate order, John Wheeler’s vision of the ‘Participatory Universe’, Henry Stapp’s account of the Heisenberg-von Neumann quantum ‘ontology’, Wojciech Zurek’s ‘Quantum Darwinism’ proposal and the Buddhist Mind-Only (Yogachara–Chittamatra) concept of the alayavijnana, the gro…