Relation between Optical Fresnel transformation and quantum tomography in two-mode entangled case

Similar in spirit to the preceding work [Opt. Commun. 282 (2009) 3734] where the relation between optical Fresnel transformation and quantum tomography is revealed, we study this kind of relationship in the two-mode entangled case. We show that under the two-mode Fresnel transformation the bipartite entangled state density |eta><eta|F_2 ^{dag}=|eta>_{r,s}<eta|, which is just the Radon transform of the two-mode Wigner operator (sigma,gama) in entangled form, where F_2 is an two-mode Fresnel operator in quantum optics, and s,r are the complex-value expression of (A, B, C,D). So the probability distribution for the Fresnel quadrature phase is the {tomography (Radon transform of the two-mode Wigner function), correspondingly, {s,r}_=. Similarly, we find a simial conclusion in the `frequency` domain.Comment: 10 page

Collins diffraction formula and the Wigner function in entangled state representation

Based on the correspondence between Collins diffraction formula (optical Fresnel transform) and the transformation matrix element of a three-parameters two-mode squeezing operator in the entangled state representation (Opt. Lett. 31 (2006) 2622) we further explore the relationship between output field intensity determined by the Collins formula and the input field's probability distribution along an infinitely thin phase space strip both in spacial domain and frequency domain. The entangled Wigner function is introduced for recapitulating the result.Comment: 6 pages, no figur

Density matrix of the superposition of excitation on coherent states with thermal light and its statistical properties

A beam's density matrix that is described by the superposition of excitation on coherent states with thermal noise (SECST) is presented, and its matrix elements in Fock space are calculated. The maximum information transmitted by the SECST beam is derived. It is more than that by coherent light beam and increases as the excitation photon number increases. In addition, the nonclassicality of density matrix is demonstrated by calculating its Wigner function.Comment: 7 pages, 9 figures, revtex

Laguerre-Gaussian modes: entangled state representation and generalized Wigner transform in quantum optics

By introducing a new entangled state representation, we show that the Laguerre-Gaussian (LG) mode is just the wave function of the common eigenvector of the orbital angular momentum and the total photon number operators of 2-d oscillator, which can be generated by 50:50 beam splitter with the phase difference phi=Pi/2{\phi} between the reflected and transmitted fields. Based on this and using the Weyl ordering invariance under similar transforms, the Wigner representation of LG is directly obtained, which can be considered as the generalized Wigner transform of Hermite Gaussian modes.Comment: 10 pages, no figur

A new quantum mechanical photon counting distribution formula

By virtue of density operator's P-representation in the coherent state representation, we derive a new quantum mechanical photon counting distribution formula. As its application, we find the photon counting distribution for the pure squeezed state relates to the Legendre function, which seems a new result.Comment: 6 pages, 0 figure

Realizing degree sequences as Z3Z_3-connected graphs

An integer-valued sequence $\pi=(d_1, \ldots, d_n)$ is {\em graphic} if there is a simple graph $G$ with degree sequence of $\pi$. We say the $\pi$ has a realization $G$. Let $Z_3$ be a cyclic group of order three. A graph $G$ is {\em $Z_3$-connected} if for every mapping $b:V(G)\to Z_3$ such that $\sum_{v\in V(G)}b(v)=0$, there is an orientation of $G$ and a mapping $f: E(G)\to Z_3-\{0\}$ such that for each vertex $v\in V(G)$, the sum of the values of $f$ on all the edges leaving from $v$ minus the sum of the values of $f$ on the all edges coming to $v$ is equal to $b(v)$. If an integer-valued sequence $\pi$ has a realization $G$ which is $Z_3$-connected, then $\pi$ has a {\em $Z_3$-connected realization} $G$. Let $\pi=(d_1, \ldots, d_n)$ be a graphic sequence with $d_1\ge \ldots \ge d_n\ge 3$. We prove in this paper that if $d_1\ge n-3$, then either $\pi$ has a $Z_3$-connected realization unless the sequence is $(n-3, 3^{n-1})$ or is $(k, 3^k)$ or $(k^2, 3^{k-1})$ where $k=n-1$ and $n$ is even; if $d_{n-5}\ge 4$, then either $\pi$ has a $Z_3$-connected realization unless the sequence is $(5^2, 3^4)$ or $(5, 3^5)$

Majorana-time-reversal symmetries: a fundamental principle for sign-problem-free quantum Monte Carlo simulations

A fundamental open issue in physics is whether and how the fermion sign problem in quantum Monte Carlo (QMC) simulations can be solved generically. Here, we show that Majorana-time-reversal (MTR) symmetries can provide a unifying principle to solve the fermion sign problem in interacting fermionic models. By systematically classifying Majorana-bilinear operators according to the anti-commuting MTR symmetries they respect, we rigorously proved that there are two and only two fundamental symmetry classes which are sign-problem-free and which we call the "Majorana class" and "Kramers class", respectively. Novel sign-problem-free models in the Majorana class include interacting topological superconductors and interacting models of charge-4e superconductors. We believe that our MTR unifying principle could shed new light on sign-problem-free QMC simulation on strongly correlated systems and interacting topological matters.Comment: Accepted by Phys. Rev. Lett. Added more references and moved part of the paper into the Supplemental Materia

Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions

Quantum critical phenomena may be qualitatively different when massless Dirac fermions are present at criticality. Using our recently-discovered fermion-sign-free Majorana quantum Monte Carlo (MQMC) method introduced by us in Ref. [1], we investigate the quantum critical phenomena of {\it spinless} Dirac fermions at their charge-density-wave (CDW) phase transitions on the honeycomb lattice having $N_s=2L^2$ sites with largest $L=24$. By finite-size scaling, we accurately obtain critical exponents of this so-called Gross-Neveu chiral-Ising universality class of {\it two} (two-component) Dirac fermions in 2+1D: $\eta=0.45(2)$, $\nu=0.77(3)$, and $\beta=0.60(3)$, which are qualitatively different from the mean-field results but are reasonably close to the ones obtained from renormalization group calculations.Comment: 5.3 pages, Published as part of "Focus on Topological Physics: From Condensed Matter to Cold Atoms and Optics" in New Journal of Physic

Solving fermion sign problem in quantum Monte Carlo by Majorana representation

In this paper, we discover a new quantum Monte Carlo (QMC) method to solve the fermion sign problem in interacting fermion models by employing Majorana representation of complex fermions. We call it "Majorana QMC" (MQMC). Especially, MQMC is fermion sign free in simulating a class of spinless fermion models on bipartite lattices at half filling and with arbitrary range of (unfrustrated) interactions. To the best of our knowledge, MQMC is the first auxiliary field QMC method to solve fermion sign problem in spinless (more generally, odd number of species) fermion models. MQMC simulations can be performed efficiently both at finite and zero temperatures. We believe that MQMC could pave a new avenue to solve fermion sign problem in more generic fermionic models.Comment: Selected as an Editors' Suggestion in PRB Rapid Communication, published version with updated referenc

Statistical properties and decoherence of two-mode photon-subtracted squeezed vacuum

We investigate the statistical properties of the photon-subtractions from the two-mode squeezed vacuum state and its decoherence in a thermal environment. It is found that the state can be considered as a squeezed two-variable Hermite polynomial excitation vacuum and the normalization of this state is the Jacobi polynomial of the squeezing parameter. The compact expression for Wigner function (WF) is also derived analytically by using the Weyl ordered operators' invariance under similar transformations. Especially, the nonclassicality is discussed in terms of the negativity of WF. The effect of decoherence on this state is then discussed by deriving the analytical time evolution results of WF. It is shown that the WF is always positive for any squeezing parameter and photon-subtraction number if the decay time exceeds an upper bound (}$\kappa t>{1/2}\ln \frac{2\bar{n}+2}{2\bar{n}+1}).Comment: 17 pages, 11 figure