Session U02: Advances in Matter-Wave Entanglement and Spin-Squeezing

Spin-squeezing for alkali earth atom interferometers

Today, matter-wave interferometers as clocks and gravimeters allow for precision measurements of time and gravity at unprecedented levels [1].  In all these sensors, the exquisite control of both internal (electronic) and external (center of mass motion) degrees of freedom of ultra-cold atomic samples, enable us to study interactions at their most basic, quantum level, paving the way for new tests of fundamental physics. 

However, despite all the efforts done so far, highest precision clocks and interferometers have not taken full advantage from the quantum properties of matter waves, yet. Here, we present alternative schemes for the production and the use of metrologically useful entanglement in cold-atom systems, through the coupling of atoms with a high-finesse optical cavity. All these schemes rely on the use of narrow optical intercombination transitions in alkali-earth atoms, recently employed in new generation atom interferometers based on single photon (clock) and two photon (Bragg) interaction [2,3,4].

The presence of high coherence internal states connected with such high relative frequency resolution, makes these atoms very good candidates for the actual implementation of spin-squeezing schemes on their internal and external degrees of freedom, free from decoherence [5,6]. Here, in particular, I’ll show the work we’ve been doing so far towards the realization of an experimental apparatus for the production of a spin squeezed source based on strontium atoms with direct application in Bragg and clock interferometers.

Moreover, the experimental results toward the production of ultra-cold cadmium for atom interferometry and prospects for tests of fundamental physics will also be discussed [7,8].

    

Nonlinear nano-optical devices based on coupled quantum emitter arrays

Subwavelength arrays of quantum emitters feature unique and largely designable nonlinear optical properties. In particular, absorption and emission properties of nanoscopic ring structures offer unique possibilities. As striking example we identify a sub-wavelength sized ring of exactly 9 identical dipoles with an extra identical emitter with a extra loss channel at the center as the most efficient antenna configuration to direct incoming photons to the center without reemission.

The enhancement is most pronounced a given resonance frequency but still stays visible for broadband light absorption. For very tiny structures below a tenth of a wavelength a full quantum description exhibits a larger enhancement than predicted from a classical dipole approximation.

The origin of the effect lies in the appearance of a collective dark state with dominant center occupation. By special design of the center absorber one can harness the same efficiency enhancement also at different wavelengths and for other geometric structures.

On the one hand this could be the basis of a new generation of highly efficient and selective nano antennas while on the other hand it could be an important piece towards understanding the surprising efficiency of natural light harvesting molecules. Adding gain in nano ring systems allows to design minimalistic classical as well as non-classical light sources.   

Entanglement-Enhanced Matter-Wave Interferometry in a High-Finesse Cavity

Entanglement is a fundamental resource that allows quantum sensors to surpass the standard quantum limit set by the quantum collapse of independent atoms. Collective cavity-QED systems have succeeded in generating large amounts of directly observed entanglement involving the internal degrees of freedom of laser-cooled atomic ensembles. Here we demonstrate cavity-QED entanglement of external degrees of freedom to realize a matter-wave interferometer of 700 atoms in which each individual atom falls freely under gravity and simultaneously traverses two paths through space while also entangled with the other atoms. We demonstrate both quantum non-demolition measurements and cavity-mediated spin interactions for generating squeezed momentum states with directly observed metrological gain 3.4 dB and 2.5 dB below the standard quantum limit respectively. An entangled state is successfully injected into a Mach-Zehnder light-pulse interferometer with 1.7 dB of directly observed metrological enhancement. These results open a new path for combining particle delocalization and entanglement for inertial sensors, searches for new physics, particles, and fields, future advanced gravitational wave detectors, and accessing beyond mean-field quantum many-body physics.   

A phase diagram for quantum states with adjustable energy

Depending on external control parameters, the physically realized states of a given system can be grouped into phases that are defined by a measurable order parameter. For ultracold systems, where quantum fluctuations dominate thermal fluctuations, quantum phases arise, which are separated by quantum phase transitions (QPTs) with a vanishing energy gap between the ground state and the first excited state. Today, ultracold quantum many-body systems can also be prepared at non-zero energy and protected from the environment to suppress thermalization. For such systems, it is possible to define excited-state quantum phase transitions (ESQPTs) by an analogous divergence of the density of states. While signatures of such singularities were detected in molecular spectra [1-3], an experimental classification of excited-state quantum phases has not yet been demonstrated.

Here we present the experimental determination of a quantum phase diagram, where the energy of the system is one of the control parameters. The quantum phases are detected by the measurement of an interferometric order parameter [4] that abruptly changes at the ESQPTs. The concept is demonstrated with an atomic Bose-Einstein condensate with a spin degree of freedom. We show that the three ground-state phases that appear as a function of the effective magnetic field, are zero-energy boundaries of equivalent excited-state quantum phases. We pinpoint the excited-state phase transitions by varying three order parameters: the energy, the effective magnetic field, and an adjustable phase between the spin components. Our work presents an example how the extensive Hilbert state of quantum many-body systems can be structured by the definition and measurement of well-defined order parameters.

[1] B. P. Winnewisser, et al., Phys. Rev. Lett. 95, 243002 (2005).

[2] N. F. Zobov, et al., Chem. Phys. Lett. 414, 193 (2005).

[3] D. Larese, F. Pérez-Bernal, F. Iachello, J. Mol. Struct. 1051, 310 (2013).

[4] P. Feldmann, et al., Phys. Rev. Lett. 126, (2021)