647,157 research outputs found

### Phase Operator for the Photon Field and an Index Theorem

An index relation $dim\ ker\ a^{\dagger}a - dim\ ker\ aa^{\dagger} = 1$ is
satisfied by the creation and annihilation operators $a^{\dagger}$ and $a$ of a
harmonic oscillator. A hermitian phase operator, which inevitably leads to
$dim\ ker\ a^{\dagger}a - dim\ ker\ aa^{\dagger} = 0$, cannot be consistently
defined. If one considers an $s+1$ dimensional truncated theory, a hermitian
phase operator of Pegg and Barnett which carries a vanishing index can be
defined. However, for arbitrarily large $s$, we show that the vanishing index
of the hermitian phase operator of Pegg and Barnett causes a substantial
deviation from minimum uncertainty in a characteristically quantum domain with
small average photon numbers. We also mention an interesting analogy between
the present problem and the chiral anomaly in gauge theory which is related to
the Atiyah-Singer index theorem. It is suggested that the phase operator
problem related to the above analytic index may be regarded as a new class of
quantum anomaly. From an anomaly view point ,it is not surprising that the
phase operator of Susskind and Glogower, which carries a unit index, leads to
an anomalous identity and an anomalous commutator.Comment: 32 pages, Late

### Clustering of exceptional points and dynamical phase transitions

The eigenvalues of a non-Hermitian Hamilton operator are complex and provide
not only the energies but also the lifetimes of the states of the system. They
show a non-analytical behavior at singular (exceptional) points (EPs). The
eigenfunctions are biorthogonal, in contrast to the orthogonal eigenfunctions
of a Hermitian operator. A quantitative measure for the ratio between
biorthogonality and orthogonality is the phase rigidity of the wavefunctions.
At and near an EP, the phase rigidity takes its minimum value. The lifetimes of
two nearby eigenstates of a quantum system bifurcate under the influence of an
EP. When the parameters are tuned to the point of maximum width bifurcation,
the phase rigidity suddenly increases up to its maximum value. This means that
the eigenfunctions become almost orthogonal at this point. This unexpected
result is very robust as shown by numerical results for different classes of
systems. Physically, it causes an irreversible stabilization of the system by
creating local structures that can be described well by a Hermitian Hamilton
operator. Interesting non-trivial features of open quantum systems appear in
the parameter range in which a clustering of EPs causes a dynamical phase
transition.Comment: A few improvements; 2 references added; 28 pages; 7 figure

### Imposing det E > 0 in discrete quantum gravity

We point out that the inequality det E > 0 distinguishes the kinematical
phase space of canonical connection gravity from that of a gauge field theory,
and characterize the eigenvectors with positive, negative and zero-eigenvalue
of the corresponding quantum operator in a lattice-discretized version of the
theory. The diagonalization of the operator det E is simplified by classifying
its eigenvectors according to the irreducible representations of the octagonal
group.Comment: 10 pages, plain Te

### Hole-Doping Effects on a Two-dimensional Kondo Insulator

We study the effects of hole doping on the two-dimensional Heisenberg-Kondo
model around the quantum critical point, where the spin liquid phase (Kondo
insulator) and the magnetically ordered phase are separated via a second-order
phase transition. By means of the self-consistent Born approximation within the
bond operator formalism as well as the standard spin wave theory, we discuss
dynamical properties of a doped hole. It is clarified that a quasi-particle
state stabilized in the spin liquid phase is gradually obscured as the system
approaches the quantum critical point. This is also the case for the
magnetically ordered phase. We argue the similarity and the difference between
these two cases.Comment: 8 pages, 14 figure

### Direct measurement of the Wigner function by photon counting

We report a direct measurement of the Wigner function characterizing the
quantum state of a light mode. The experimental scheme is based on the
representation of the Wigner function as an expectation value of a displaced
photon number parity operator. This allowed us to scan the phase space
point-by-point, and obtain the complete Wigner function without using any
numerical reconstruction algorithms.Comment: 4 pages, REVTe

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