# Quantum simulations with circular Rydberg atoms

##### Recent publications

♦ Laser Trapping of circular Rydberg atoms

R. Cortiñas, M. Favier, B. Ravon, P. Méhaignerie, Y. Machu, J.M. Raimond, C. Sayrin and M. Brune

arXiv:02316 (2019)

♦ Towards quantum simulation with circular Rydberg atoms

T.L. Nguyen, J.M. Raimond, C. Sayrin, R. Cortiñas, T. Cantat-Moltrecht, F. Assemat, I. Dotsenko, S. Gleyzes, S. Haroche, G. Roux, T. Jolicœur and M. Brune

Phys. Rev. X 8, 011032 (2018)

**PEOPLE**

**Permanents:** Clément Sayrin, Michel Brune, Jean-Michel Raimond, Serge Haroche**PhDs:** Rodrigo Cortiñas, Brice Ravon, Paul Méhaignerie, Yohann Machu**Postdoc: **Maxime Favier

## Quantum simulations with circular Rydberg atoms

Thanks to their large electric polarizabilities, Rydberg atoms interact very strongly through dipole-dipole interactions. At a few micrometres distance, this interaction can be still as big as several MHz. The so-called dipole blockade is one of the most striking consequences of this interaction strength: the presence of a Rydberg atom prevents the excitation of a subsequent Rydberg atom in its immediate proximity.

Rydberg atoms, which can be laser-excited from alkali atoms in their ground states, and which are long-lived (several 100µs lifetime), are thus ideal candidates for the study of spin-spin interactions in dense systems. In particular, they can be used to realise a quantum simulator of condensed-matter systems.

In our group, we prepare a gas of Rydberg atoms in the vicinity of a superconducting atomchip. Rydberg atoms are excited from a gas of laser-cooled Rubidium-87 atoms, initially trapped in a magnetic trap created by the atomchip. Our work focuses on the realisation of a quantum simulator that exploits the unique properties of circular Rydberg atoms. They can be efficiently laser-trapped in spontaneous emission-inhibiting structure, thereby reaching lifetimes on the order of a minute! This should enable, e.g., the study of the dynamics of condensed-matter systems over extremely long times (about \(10^4-10^5\) interaction cycles), their response to quenches or their thermalisation properties.

LATEST NEWS

EVENTS

Tigrane’s PhD Defence## 11/01/2018

Tigrane has successfully defended his PhD thesis entitled **Interacting Rydberg Atoms : from Dense Clouds of Rydberg Atoms to Quantum Simulation with Circular Atoms** in front of a jury composed of Robin Kaiser, Leticia Tarruell, Jérôme Tignon and Matthias Weidemüller, and his supervisors Michel Brune and Clément Sayrin.

We wish him all the best for his future research activities!

Here are some pictures of this important event for the team!

RESEARCH

## Towards quantum simulation with circular Rydberg atoms

##### Publications

♦ Towards quantum simulation with circular Rydberg atoms

T.L. Nguyen, J.-M. Raimond, C. Sayrin, R. Cortinas, T. Cantat-Moltrecht, F. Assemat, I. Dotsenko, S. Gleyzes, S. Haroche, G. Roux, T. Jolicoeur, M. Brune

Phys. Rev. X 8, 011032 (2018)

##### Supplementary Materials

## Towards quantum simulation with circular Rydberg atoms

The main objective of quantum simulation is an in-depth understanding of many-body physics. It is important for fundamental issues (quantum phase transitions, transport, . . . ) and for the development of innovative materials. Analytic approaches to many-body systems are limited and the huge size of their Hilbert space makes numerical simulations on classical computers intractable. A quantum simulator avoids these limitations by transcribing the system of interest into another, with the same dynamics but with interaction parameters under control and with experimental access to all relevant observables. Quantum simulation of spin systems is being explored with a large variety of experimental systems. Some of the most advanced ones rely on trapped ion systems, superconducting circuits, trapped ultra-cold ground state atoms or even atoms excited to low angular momentum Rydberg levels.

We propose a new paradigm for quantum simulation of spin-1/2 arrays providing unprecedented flexibility and allowing one to explore domains beyond the reach of other platforms. It is based on laser-trapped circular Rydberg atoms.

The intrinsic lifetime of circular Rydberg atoms lies in the ms-range. This very long lifetime stems from the fact that a circular Rydberg atoms \( |nC\rangle\) can only decay to the \( |(n-1)C\rangle\) circular Rydberg level by the emission of a microwave photon of wavelength \(\lambda\). By placing a circular Rydberg atom in a plane-parallel condenser of size \(d\leq\lambda/2\), spontaneous emission can be efficiently inhibited and the lifetime of the circular level increased by several orders of magnitude.

In addition, while photoionisation is a severe limitation for laser trapping of low-angular momentum Rydberg levels, circular Rydberg levels do not photoionise. The combination of a Laguerre-Gaussian beam (lateral confinement) and of two crossed Gaussian beams (longitudinal confinement) then realise a very efficient trap for the low-field seeking circular Rydberg levels. Trapping lifetimes in the minute range are realistic with state-of-the-art techniques.

Finally, using an innovative approach, namely a van der Waals variant of the evaporative cooling method, ultra-cold defect-free circular atom chains containing several tens of atoms can be prepared. A chain of about 40 atoms can be deterministically prepared using this method. Its lifetime is on the range of seconds! This method also leads to the individual detection of arbitrary spin observables and, thus, to the measurement of spin-spin correlation functions.

The proposed simulator realises an XXZ spin-1/2 Hamiltonian with nearest-neighbor couplings ranging from a few to tens of kHz. The simulated Hamiltonian takes the general form

\( H/h = \frac{\Delta}{2}\sum_{i=1}^N \sigma_i^z + \frac{\Omega_0}{2}\sum_{i=1}^N \sigma_i^x + J_z \sum_{i=1}^{N-1} \sigma_i^z \sigma_{i+1}^z + J \sum_{i=1}^{N-1} \sigma_i^x \sigma_{i+1}^x + \sigma_i^y \sigma_{i+1}^y. \)

All the model parameters can be tuned at will, making a large range of simulations accessible. In particular, by a mere tuning of an electric and a magnetic field, the ratio \(J_z/J\) can be tuned from -3 to 3. The accessible phase diagram is extremely rich. The typical interaction time, \(1/4J\), is on the order of \(15\mu\mathrm{s}\). The system evolution can thus be followed over \(10^4\) to \(10^5\) interaction cycles, long enough to be relevant for ground-state adiabatic preparation and for the study of thermalization, disorder or Floquet time crystals. This platform presents unrivaled features for quantum simulation.

## Dipole blockade and microwave spectroscopy

##### Publications

♦ Microwaves Probe Dipole Blockade and van der Waals Forces in a Cold Rydberg Gas

R. Teixeira, C. Hermann-Avigliano, T.-L. Nguyen, T. Cantat-Moltrecht, J.-M. Raimond, S. Haroche, S. Gleyzes, M. Brune

Phys. Rev. Lett. 115, 013001 (2015)

##### Supplementary Materials

## Dipole blockade and microwave spectroscopy

Because of their strong electric polarizability, Rydberg atoms interact very strongly through dipole-dipole interaction. During a resonant laser excitation of Rydberg levels in a dense atomic cloud, the strength of the interaction leads to the so-called dipole blockade effect [Lukin et al. (2001)]: every Rydberg atoms is surrounded by a blockade sphere into which no other Rydberg atom can be excited. At saturation, the distance between the Rydberg atoms then corresponds to the radius of this sphere, the so-called blockade radius. However, when the laser excitation is detuned from resonance, the dipole interaction can facilitate the excitation of a Rydberg atom at a distance called facilitation radius from an initial Rydberg seed. The value of the facilitation radius is controlled via the detuning of the excitation light.

In our experiments, we have been recently able to demonstrate that the relative distance between Rydberg atoms excited in a cold gas of atoms, trapped in the vicinity of our atomchip, can be controlled via the detuning of the excitation laser. Using microwave spectroscopy, we have measured directly the interaction energy distribution of the Rydberg gas, from which we can deduce the Rydberg atoms spatial distribution. By recording the time evolution of the interaction energy distribution, we have also observed the dynamics of the Rydberg gas, which expands due to the strong repulsive interaction between the atoms. In particular, we have been able to observe the breakdown of the frozen gas approximation, few µs only after the preparation of the Rydberg gas.