Monopoles near the Planck Scale and Unification

Considering our (3+1)-dimensional space-time as, in some way, discrete or l attice with a parameter $a=\lambda_P$, where $\lambda_P$ is the Planck length, we have investigated the additional contributions of lattice artifact monopoles to beta-functions of the renormalisation group equations for the running fine structure constants $\alpha_i(\mu)$ (i=1,2,3 correspond to the U(1), SU(2) and SU(3) gauge groups of the Standard Model) in the Family Replicated Gauge Group Model (FRGGM) which is an extension of the Standard Model at high energies. It was shown that monopoles have $N_{fam}$ times smaller magnetic charge in FRGGM than in SM ($N_{fam}$ is the number of families in FRGGM). We have estimated al so the enlargement of a number of fermions in FRGGM leading to the suppression of the asymptotic freedom in the non-Abelian theory. We have shown that, in contrast to the case of AntiGUT when the FRGGM undergoes the breakdown at $\mu=\mu_G\sim 10^{18}$ GeV, we have the possibility of unification if the FRGGM-breakdown occurs at $\mu_G\sim 10^{14}$ GeV. By numerical calculations we obtained an example of the unification of all gauge interactions (including gravity) at the scale $\mu_{GUT}\approx 10^{18.4}$ GeV. We discussed the possibility of $[SU(5)]^3$ or $[SO(10)]^3$ (SUSY or not SUSY) unifications.Comment: 49 pages, 7 figure

Dephasing effects on stimulated Raman adiabatic passage in tripod configurations

We present an analytic description of the effects of dephasing processes on stimulated Raman adiabatic passage in a tripod quantum system. To this end, we develop an effective two-level model. Our analysis makes use of the adiabatic approximation in the weak dephasing regime. An effective master equation for a two-level system formed by two dark states is derived, where analytic solutions are obtained by utilizing the Demkov-Kunike model. From these, it is found that the fidelity for the final coherent superposition state decreases exponentially for increasing dephasing rates. Depending on the pulse ordering and for adiabatic evolution the pulse delay can have an inverse effect.Comment: 13 pages; 9 figures; Accepted for publication Physical Review

Scaling the neutral atom Rydberg gate quantum computer by collective encoding in Holmium atoms

We discuss a method for scaling a neutral atom Rydberg gate quantum processor to a large number of qubits. Limits are derived showing that the number of qubits that can be directly connected by entangling gates with errors at the $10^{-3}$ level using long range Rydberg interactions between sites in an optical lattice, without mechanical motion or swap chains, is about 500 in two dimensions and 7500 in three dimensions. A scaling factor of 60 at a smaller number of sites can be obtained using collective register encoding in the hyperfine ground states of the rare earth atom Holmium. We present a detailed analysis of operation of the 60 qubit register in Holmium. Combining a lattice of multi-qubit ensembles with collective encoding results in a feasible design for a 1000 qubit fully connected quantum processor.Comment: 6 figure

Weakly bound dimers of fermionic atoms

We discuss the behavior of weakly bound bosonic dimers formed in a cold Fermi gas at a large positive scattering length $a$ for the interspecies interaction. We find the exact solution for the dimer-dimer elastic scattering and obtain a strong decrease of their collisional relaxation and decay with increasing $a$. The large ratio of the elastic to inelastic rate is promising for achieving Bose-Einstein condensation of the dimers and cooling the condensed gas to very low temperatures.Comment: 4 pages, no figure

Fidelity Between Partial States as Signature of Quantum Phase Transitions

We introduce a partial state fidelity approach to quantum phase transitions. We consider a superconducting lattice with a magnetic impurity inserted at its centre, and look at the fidelity between partial (either one-site or two-site) quantum states. In the vicinity of the point of the quantum phase transition, we observe a sudden drop of the fidelity between two one-site partial states corresponding to the impurity location and its close vicinity. In the case of two-site states, the fidelity reveals the transition point as long as one of the two electron sites is located at the impurity, while the other lies elsewhere in the lattice. We also determine the Uhlmann mixed state geometric phase, recently introduced in the study of the structural change of the system state eigenvectors in the vicinity of the lines of thermal phase transitions, and find it to be trivial, both for one- and two-site partial states, except when an electron site is at the impurity. This means that the system partial state eigenvectors do not contribute significantly to the enhanced state distinguishability around the point of this quantum phase transition. Finally, we use the fidelity to analyze the total amount of correlations contained within a composite system, showing that, even for the smallest two-site states, it features an abrupt quantitative change in the vicinity of the point of the quantum phase transition.Comment: 11 pages, 5 figure

Solutions of the Ginsparg-Wilson Relation

We analyze general solutions of the Ginsparg-Wilson relation for lattice Dirac operators and formulate a necessary condition for such operators to have non-zero index in the topologically nontrivial background gauge fields.Comment: 6 pages, latex, no figures, set T to 1 in eqs. (10)--(13

Suppression of Decoherence and Disentanglement by the Exchange Interaction

Entangled qubit pairs can serve as a quantum memory or as a resource for quantum communication. The utility of such pairs is measured by how long they take to disentangle or decohere. To answer the question of whether qubit-qubit interactions can prolong entanglement, we calculate the dissipative dynamics of a pair of qubits coupled via the exchange interaction in the presence of random telegraph noise and $1/f$ noise. We show that for maximally entangled (Bell) states, the exchange interaction generally suppresses decoherence and disentanglement. This suppression is more apparent for random telegraph noise if the noise is non-Markovian, whereas for $1/f$ noise the exchange interaction should be comparable in magnitude to strongest noise source. The entangled singlet-triplet superposition state of 2 qubits ($\psi_{\pm}$ Bell state) can be protected by the interaction, while for the triplet-triplet state ($\phi_{\pm}$ Bell state), it is less effective. Thus the former is more suitable for encoding quantum information

Heat kernel of non-minimal gauge field kinetic operators on Moyal plane

We generalize the Endo formula originally developed for the computation of the heat kernel asymptotic expansion for non-minimal operators in commutative gauge theories to the noncommutative case. In this way, the first three non-zero heat trace coefficients of the non-minimal U(N) gauge field kinetic operator on the Moyal plane taken in an arbitrary background are calculated. We show that the non-planar part of the heat trace asymptotics is determined by U(1) sector of the gauge model. The non-planar or mixed heat kernel coefficients are shown to be gauge-fixing dependent in any dimension of space-time. In the case of the degenerate deformation parameter the lowest mixed coefficients in the heat expansion produce non-local gauge-fixing dependent singularities of the one-loop effective action that destroy the renormalizability of the U(N) model at one-loop level. The twisted-gauge transformation approach is discussed.Comment: 21 pages, misprints correcte

Why Nature has made a choice of one time and three space coordinates?

We propose a possible answer to one of the most exciting open questions in physics and cosmology, that is the question why we seem to experience four- dimensional space-time with three ordinary and one time dimensions. We have known for more than 70 years that (elementary) particles have spin degrees of freedom, we also know that besides spin they also have charge degrees of freedom, both degrees of freedom in addition to the position and momentum degrees of freedom. We may call these ''internal degrees of freedom '' the ''internal space'' and we can think of all the different particles, like quarks and leptons, as being different internal states of the same particle. The question then naturally arises: Is the choice of the Minkowski metric and the four-dimensional space-time influenced by the ''internal space''? Making assumptions (such as particles being in first approximation massless) about the equations of motion, we argue for restrictions on the number of space and time dimensions. (Actually the Standard model predicts and experiments confirm that elementary particles are massless until interactions switch on masses.) Accepting our explanation of the space-time signature and the number of dimensions would be a point supporting (further) the importance of the ''internal space''.Comment: 13 pages, LaTe

Conservation and entanglement of Hermite-Gaussian modes in parametric down-conversion

We show that the transfer of the angular spectrum of the pump beam to the two-photon state in spontaneous parametric down-conversion enables the generation of entangled Hermite-Gaussian modes. We derive an analytical expression for the two-photon state in terms of these modes and show that there are restrictions on both the parity and order of the down-converted Hermite-Gaussian fields. Using these results, we show that the two-photon state is indeed entangled in Hermite-Gaussian modes. We propose experimental methods of creating maximally-entangled Bell states and non-maximally entangled pure states of first order Hermite-Gaussian modes.Comment: 9 pages, 4 figures. Corrections made as per referee comments, references updated. Submitted PR