Optimal control for one-qubit quantum sensing

Quantum systems can be exquisite sensors thanks to their sensitivity to external perturbations. This same characteristic also makes them fragile to external noise. Quantum control can tackle the challenge of protecting quantum sensors from environmental noise, while leaving their strong coupling to the target field to be measured. As the compromise between these two conflicting requirements does not always have an intuitive solution, optimal control based on numerical search could prove very effective. Here we adapt optimal control theory to the quantum sensing scenario, by introducing a cost function that, unlike the usual fidelity of operation, correctly takes into account both the unknown field to be measured and the environmental noise. We experimentally implement this novel control paradigm using a Nitrogen Vacancy center in diamond, finding improved sensitivity to a broad set of time varying fields. The demonstrated robustness and efficiency of the numerical optimization, as well as the sensitivity advantaged it bestows, will prove beneficial to many quantum sensing applications

Static quantum corrections to the Schwarzschild spacetime

We study static quantum corrections of the Schwarzschild metric in the Boulware vacuum state. Due to the absence of a complete analytic expression for the full semiclassical Einstein equations we approach the problem by considering the s-wave approximation and solve numerically the associated backreaction equations. The solution, including quantum effects due to pure vacuum polarization, is similar to the classical Schwarzschild solution up to the vicinity of the classical horizon. However, the radial function has a minimum at a time-like surface close to the location of the classical event horizon. There the g_{00} component of the metric reaches a very small but non-zero value. The analysis unravels how a curvature singularity emerges beyond this bouncing point. We briefly discuss the physical consequences of these results by extrapolating them to a dynamical collapsing scenario.Comment: 10 pages; Talk given at QG05, Cala Gonone (Italy), September 200

Probing correlations of gaseous microwires in lattice potentials via inelastic light scattering

In this work, inelastic light-scattering (Bragg spectroscopy) is used to study strongly correlated phases of ultracold 1D gases in optical lattices. We investigate the crossover from correlated superfluids to Mott insulators. Light-scattering creates in the system elementary excitations with non-zero momentum, and the response of the correlated gases is in the linear regime. This allows for extracting information about the atomic many-body state in terms of its particle-hole excitations, as common in solid-state physics. In particular, we characterize the Mott state both via intra-band and inter-band spectroscopy, the former giving access to the dynamical structure factor S(q, ω) and the latter to the one-particle spectral function A(q, ω)

Multi-band spectroscopy of inhomogeneous Mott-insulator states of ultracold bosons

In this work, we use inelastic scattering of light to study the response of inhomogeneous Mott-insulator gases to external excitations. The experimental setup and procedure to probe the atomic Mott states are presented in detail. We discuss the link between the energy absorbed by the gases and accessible experimental parameters as well as the linearity of the response to the scattering of light. We investigate the excitations of the system in multiple energy bands and a band-mapping technique allows us to identify band and momentum of the excited atoms. In addition the momentum distribution in the Mott states which is spread over the entire first Brillouin zone enables us to reconstruct the dispersion relation in the high energy bands using a single Bragg excitation with a fixed momentum transfer.Comment: 19 pages, 7 figure

Quantum effects in Acoustic Black Holes: the Backreaction

We investigate the backreaction equations for an acoustic black hole formed in a Laval nozzle under the assumption that the motion of the fluid is one-dimensional. The solution in the near-horizon region shows that as phonons are (thermally) radiated the sonic horizon shrinks and the temperature decreases. This contrasts with the behaviour of Schwarzschild black holes, and is similar to what happens in the evaporation of (near-extremal) Reissner-Nordstrom black holes (i.e. infinite evaporation time). Finally, by appropriate boundary conditions the solution is extended in both the asymptotic regions of the nozzle.Comment: 23 pages, latex, 1 figure; revised version, to appear in Phys. Rev.

Hawking radiation from extremal and non-extremal black holes

The relationship between Hawking radiation emitted by non extremal and extremal Reissner Nordstrom black holes is critically analyzed. A careful study of a series of regular collapsing geometries reveals that the stress energy tensor stays regular in the extremal limit and is smoothly connected to that of non extremal black holes. The unexpected feature is that the late time transients which played little role in the non extremal case are necessary to preserve the well defined character of the flux in the extremal case. The known singular behavior of the static energy density of extremal black holes is recovered from our series by neglecting these transients, when performing what turns out to be an illegitimate late time limit. Although our results are derived in two dimensional settings, we explain why they should also apply to higher dimensional black holes.Comment: 18 pages, late

Entanglement generation in relativistic quantum fields

We present a general, analytic recipe to compute the entanglement that is generated between arbitrary, discrete modes of bosonic quantum fields by Bogoliubov transformations. Our setup allows the complete characterization of the quantum correlations in all Gaussian field states. Additionally, it holds for all Bogoliubov transformations. These are commonly applied in quantum optics for the description of squeezing operations, relate the mode decompositions of observers in different regions of curved spacetimes, and describe observers moving along non-stationary trajectories. We focus on a quantum optical example in a cavity quantum electrodynamics setting: an uncharged scalar field within a cavity provides a model for an optical resonator, in which entanglement is created by non-uniform acceleration. We show that the amount of generated entanglement can be magnified by initial single-mode squeezing, for which we provide an explicit formula. Applications to quantum fields in curved spacetimes, such as an expanding universe, are discussed.Comment: 8 pages, 2 figures, Ivette Fuentes previously published as Ivette Fuentes-Guridi and Ivette Fuentes-Schuller; v2: published version (online), to appear in the J. Mod. Opt. Special Issue on the Physics of Quantum Electronic