New transformation of Wigner operator in phase space quantum mechanics for the two-mode entangled case

As a natural extension of Fan's paper (arXiv: 0903.1769vl [quant-ph]) by employing the formula of operators' Weyl ordering expansion and the bipartite entangled state representation we find new two-fold complex integration transformation about the Wigner operator (in its entangled form) in phase space quantum mechanics and its inverse transformation. In this way, some operator ordering problems can be solved and the contents of phase space quantum mechanics can be enriched.Comment: 8 pages, 0 figure

Simultaneous eigenstates of the number-difference operator and a bilinear interaction Hamiltonian derived by solving a complex differential equation

As a continuum work of Bhaumik et al who derived the common eigenvector of the number-difference operator Q and pair-annihilation operator ab (J. Phys. A9 (1976) 1507) we search for the simultaneous eigenvector of Q and (ab-a^{+}b^{+}) by setting up a complex differential equation in the bipartite entangled state representation. The differential equation is then solved in terms of the two-variable Hermite polynomials and the formal hypergeometric functions. The work is also an addendum to Mod. Phys. Lett. A 9 (1994) 1291 by Fan and Klauder, in which the common eigenkets of Q and pair creators are discussed

Nonclassicality of photon-added squeezed vacuum and its decoherence in thermal environment

We study the nonclassicality of photon-added squeezed vacuum (PASV) and its decoherence in thermal environment in terms of the sub-Poissonian statistics and the negativity of Wigner function (WF). By converting the PASV to a squeezed Hermite polynomial excitation state, we derive a compact expression for the normalization factor of m-PASV, which is an m-order Legendre polynomial of squeezing parameter r. We also derive the explicit expression of WF of m-PASV and find the negative region of WF in phase space. We show that there is an upper bound value of r for this state to exhibit sub-Poissonian statistics increasing as m increases. Then we derive the explicit analytical expression of time evolution of WF of m-PASV in the thermal channel and discuss the loss of nonclassicality using the negativity of WF. The threshold value of decay time is presented for the single PASV.Comment: 14 pages and 7 figure

Wigner functions of thermo number state, photon subtracted and added thermo vacuum state at finite temperature

Based on Takahashi-Umezawa thermo field dynamics and the order-invariance of Weyl ordered operators under similar transformations, we present a new approach to deriving the exact Wigner functions of thermo number state, photon subtracted and added thermo vacuum state. We find that these Wigner functions are related to the Gaussian-Laguerre type functions of temperature, whose statistical properties are then analysed.Comment: 10 pages and 2 figure

Fresnel operator, squeezed state and Wigner function for Caldirola-Kanai Hamiltonian

Based on the technique of integration within an ordered product (IWOP) of operators we introduce the Fresnel operator for converting Caldirola-Kanai Hamiltonian into time-independent harmonic oscillator Hamiltonian. The Fresnel operator with the parameters A,B,C,D corresponds to classical optical Fresnel transformation, these parameters are the solution to a set of partial differential equations set up in the above mentioned converting process. In this way the exact wavefunction solution of the Schr\"odinger equation governed by the Caldirola-Kanai Hamiltonian is obtained, which represents a squeezed number state. The corresponding Wigner function is derived by virtue of the Weyl ordered form of the Wigner operator and the order-invariance of Weyl ordered operators under similar transformations. The method used here can be suitable for solving Schr\"odinger equation of other time-dependent oscillators.Comment: 6 pages, 2 figure

Energy average formula of photon gas rederived by using the generalized Hermann-Feynman theorem

By virtue of the generalized Hermann-Feynmam theorem and the method of characteristics we rederive energy average formula of photon gas, this is another useful application of the theorem.Comment: 2 page

Inversion formula and Parsval theorem for complex continuous wavelet transforms studied by entangled state representation

In a preceding Letter (Opt. Lett. 32, 554 (2007)) we have proposed complex continuous wavelet transforms (CCWTs) and found Laguerre--Gaussian mother wavelets family. In this work we present the inversion formula and Parsval theorem for CCWT by virtue of the entangled state representation, which makes the CCWT theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.Comment: 4 pages no figur

Search for gravitational waves from the coalescence of sub-solar mass binaries in the first half of Advanced LIGO and Virgo's third observing run

We present a search for gravitational waves from the coalescence of sub-solar mass black hole binaries using data from the first half of Advanced LIGO and Virgo's third observing run. The observation of a sub-solar mass black hole merger may be an indication of primordial origin; primordial black holes may contribute to the dark matter distribution. We search for black hole mergers where the primary mass is $0.1-7 M_{\odot}$ and the secondary mass is $0.1-1 M_{\odot}$. A variety of models predict the production and coalescence of binaries containing primordial black holes; some involve dynamical assembly which may allow for residual eccentricity to be observed. For component masses $>0.5 M_{\odot}$, we also search for sources in eccentric orbits, measured at a reference gravitational-wave frequency of 10 Hz, up to $e_{10}\sim 0.3$. We find no convincing candidates and place new upper limits on the rate of primordial black hole mergers. The merger rate of 0.5-0.5 (1.0-1.0)~$M_{\odot}$ sources is $<7100~(1200)$ Gpc$^{-3}$yr$^{-1}$. Our limits are $\sim3-4$ times more constraining than prior analyses. Finally, we demonstrate how our limits can be used to constrain arbitrary models of the primordial black hole mass distribution and merger rate.Comment: 7 pages, 3 figures, 1 table, v3 updated to match PRL, supplementary materials at https://github.com/gwastro/subsolar-o3a-searc

Search for Gravitational Waves from High-Mass-Ratio Compact-Binary Mergers of Stellar Mass and Subsolar Mass Black Holes

We present the first search for gravitational waves from the coalescence of stellar mass and subsolar mass black holes with masses between 20-100 M⊙ and 0.01-1 M⊙(10-103 MJ), respectively. The observation of a single subsolar mass black hole would establish the existence of primordial black holes and a possible component of dark matter. We search the ∼164 day of public LIGO data from 2015-2017 when LIGO-Hanford and LIGO-Livingston were simultaneously observing. We find no significant candidate gravitational-wave signals. Using this nondetection, we place a 90% upper limit on the rate of 30-0.01 M⊙ and 30-0.1 M⊙ mergers at <1.2×106 and <1.6×104 Gpc-3 yr-1, respectively. If we consider binary formation through direct gravitational-wave braking, this kind of merger would be exceedingly rare if only the lighter black hole were primordial in origin (<10-4 Gpc-3 yr-1). If both black holes are primordial in origin, we constrain the contribution of 1(0.1)M⊙ black holes to dark matter to <0.3(3)%. © 2021 authors

First Targeted Search for Gravitational Waves from Highly Spinning Light Compact Binaries

Searches for gravitational waves from compact-binary mergers, which to date have reported $\sim100$ observations, have previously ignored binaries whose components are both light ($<2M_\odot$) and have high dimensionless spin ($>0.05$). While previous searches targeted sources that are representative of observed neutron star binaries in the galaxy, it is already known that neutron stars can regularly be spun up to a dimensionless spin of $\sim0.4$, and in principle reach up to $\sim0.7$ before breakup would occur. Furthermore, there may be primordial black hole binaries or exotic formation mechanisms to produce subsolar mass black holes. In these cases, it is possible for the binary constituent to be spun up beyond that achievable by a neutron star. A single detection of this type of source would reveal a novel formation channel for compact-binaries. To determine if there is evidence for any such sources, we use PyCBC to conduct the first search of LIGO and Virgo data for light compact objects with high spin. Our analysis detects previously known observations GW170817 and GW200115; however, we report no additional mergers. The most significant candidate, not previously known, is consistent with the noise distribution, and so we constrain the merger rate of spinning light binaries.Comment: v2: fix typos, mention PyCBC. 6 pages, 5 figures. data release at https://github.com/gwastro/high-spin-light-binary. Comments welcome