7,050 research outputs found
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 and the secondary mass is . 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
, we also search for sources in eccentric orbits, measured at a
reference gravitational-wave frequency of 10 Hz, up to . 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)~
sources is Gpcyr. Our limits are 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 observations, have previously ignored binaries whose
components are both light () and have high dimensionless spin
(). 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 , and in
principle reach up to 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
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