407 research outputs found
Experimentally-realizable phase transitions in reflectionless quantum scattering
A class of above-barrier quantum-scattering problems is shown to provide an
experimentally-accessible platform for studying -symmetric
Schr\"odinger equations that exhibit spontaneous symmetry
breaking despite having purely real potentials. These potentials are
one-dimensional, inverted, and unstable and have the form (), terminated at a finite length or energy to a constant value
as . The signature of unbroken symmetry is the
existence of reflectionless propagating states at discrete real energies up to
arbitrarily high energy. In the -broken phase, there are no such
solutions. In addition, there exists an intermediate mixed phase, where
reflectionless states exist at low energy but disappear at a fixed finite
energy, independent of termination length. In the mixed phase exceptional
points (EPs) occur at specific and energy values, with a quartic dip in the
reflectivity in contrast to the quadratic behavior away from EPs.
-symmetry-breaking phenomena have not been previously predicted
in a quantum system with a real potential and no reservoir coupling. The
effects predicted here are measurable in standard cold-atom experiments with
programmable optical traps. The physical origin of the symmetry-breaking
transition is elucidated using a WKB force analysis that identifies the spatial
location of the above-barrier scattering
Leveraging Hamiltonian Simulation Techniques to Compile Operations on Bosonic Devices
Circuit QED enables the combined use of qubits and oscillator modes. Despite
a variety of available gate sets, many hybrid qubit-boson (i.e., oscillator)
operations are realizable only through optimal control theory (OCT) which is
oftentimes intractable and uninterpretable. We introduce an analytic approach
with rigorously proven error bounds for realizing specific classes of
operations via two matrix product formulas commonly used in Hamiltonian
simulation, the Lie--Trotter and Baker--Campbell--Hausdorff product formulas.
We show how this technique can be used to realize a number of operations of
interest, including polynomials of annihilation and creation operators, i.e.,
for integer . We show examples of this paradigm
including: obtaining universal control within a subspace of the entire Fock
space of an oscillator, state preparation of a fixed photon number in the
cavity, simulation of the Jaynes--Cummings Hamiltonian, simulation of the
Hong-Ou-Mandel effect and more. This work demonstrates how techniques from
Hamiltonian simulation can be applied to better control hybrid boson-qubit
devices.Comment: 48 pages, 5 figure
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