• M. Martinez-Valado, N. Malossi, S. Scotto, C. Simonelli, D. Ciampini • P. Huillery, P. Pillet (Paris) • E. Arimondo •Funding: COHERENCE, EMALI, PRIN

?

? Richard Feynman

? Vannevar Bush

Richard Feynman

ac network analyzers, ca. 1925-1960

network analyzer finds solutions through measurements on a scale model; effectively performs an analogue computation (later used for other calculations, e.g. elasticity, Schrodinger’s equation…)

analogue computer →

digital computer

… but 30 years later…

Feynman’s problem

Feynman’s problem

classical world

quantum world

Feynman’s problem

classical world

quantum world

A fully quantum calculation for 40 particles requires 1 TB of memory; the memory requirements for 80 particles exceed the amount of information stored in the history of mankind. Consequence: need - quantum computer or - quantum simulator = analogue quantum computer

Quantum simulators

Quantum simulators

Hˆ = ∑ Hˆ i + ∑ Uˆ jk + ∑ Vˆl + ... i

j ,k

l

Quantum simulators

Hˆ = ∑ Hˆ i + ∑ Uˆ jk + ∑ Vˆl + ... i

j ,k

l

An ideal quantum simulator

a collection of controllable quantum systems: ultra-cold atoms (MOT, BEC,..)

An ideal quantum simulator

to simulate an ordered system (crystal,…): cold atoms in optical lattices

An ideal quantum simulator

to simulate an ordered system (crystal,…): cold atoms in optical lattices. Interactions can come from onsite repulsion, Hamiltonian is then

An ideal quantum simulator

Bose-Hubbard model: superfluid to Mott insulator transition (Greiner et al., Nature 415, 39-44 (2002); Zenesini et al., PRL102, 100403 (2009))

An ideal quantum simulator

In order to study strongly correlated many-body systems, need strong interactions between nearest neighbours, next nearest neighbours… Ideally, these should be controllable to implement a range of Hamiltonians

An ideal quantum simulator

Possible solution: Excite atoms to Rydberg states

Rydberg atom

An ideal quantum simulator Lifetime: ~ n3 n=100 1 ms Polarizability ~ n7 Dipole moment : ~ n2 ea0 n=100 10,000 D (H2O ~2 D) strong van-der-Waals or dipole-dipole interaction; orders of magnitude larger than contact interaction in ultracold gases (up to GHz at micrometer distances)!

Possible solution: Excite atoms to Rydberg states

Rydberg atom

Towards a quantum simulator with cold Rydberg atoms • excitation and detection of Rydberg excitations in a cold cloud • revealing strong Rydberg-Rydberg interactions through counting statistics • using full counting statistics as a tool for gaining insight into the system • using cold Rydberg atoms to simulate a dissipative Ising system

Caveat: Even then, Feynman acknowledged that desperation for research funding was driving a tendency by scientists to hype the applications of their work. Otherwise, a friend told him, "we won't get support for more research of this kind." Feynman's reaction was characteristically blunt. "I think that's kind of dishonest," he said.

Towards a quantum simulator with cold Rydberg atoms • excitation and detection of Rydberg excitations in a cold cloud • revealing strong Rydberg-Rydberg interactions through counting statistics • using full counting statistics as a tool for gaining insight into the system • using cold Rydberg atoms to simulate a dissipative Ising system

Excitation and detection scheme

• MOT containing around 105 atoms, density 1010 cm-3, temperature 150 µK • two-photon excitation scheme (87-Rb) with Rabi frequencies up to 500 kHz • detection by field ionization; detection efficiency around 40%

Towards a quantum simulator with cold Rydberg atoms • creation and detection of Rydberg excitations in a cold cloud • revealing strong Rydberg-Rydberg interactions through counting statistics • using full counting statistics as a tool for gaining insight into the system • using cold Rydberg atoms to simulate a dissipative Ising system

Revealing strong interactions through counting statistics

Van-der-Waals interaction shifts additional excitations within the blockade volume out of resonance -> dipole blockade

Revealing strong interactions through counting statistics

Q=

N − Ne 2 e

Ne

2

−1

Q = 0 : Poissonian counting statistics

Q = − Pe ≈ −0.1

Q = − Pecoll ≈ −1

Q ≈ −1 : strongly sub-Poissonian

counting statistics indicating anti-correlation of excitations

Revealing strong interactions through counting statistics

Towards a quantum simulator with cold Rydberg atoms • creation and detection of Rydberg excitations in a cold cloud • revealing strong Rydberg-Rydberg interactions through counting statistics • using full counting statistics as a tool for gaining insight into the system • using cold Rydberg atoms to simulate a dissipative Ising system

Full counting statistics as a tool

Resonant excitation: exclusion due to dipole blockade

Off-resonant excitation: inclusion due to two-photon resonant pair excitation or singlephoton excitation of a single atom at resonant distance from an already excited one (“facilitation”)

Full counting statistics as a tool On resonance: saturation due to dipole blockade for long times

Rydberg state: 70S

Off resonance: slow growth due to pair / facilitated excitations

Full counting statistics as a tool

Towards a quantum simulator with cold Rydberg atoms • creation and detection of Rydberg excitations in a cold cloud • revealing strong Rydberg-Rydberg interactions through counting statistics • using full counting statistics as a tool for gaining insight into the system • using cold Rydberg atoms to simulate a dissipative Ising system

Simulating a dissipative Ising system

Simulating a dissipative Ising system

Simulating a dissipative Ising system

• on resonance, the distribution becomes highly sub-Poissonian for large mean numbers • off resonance, the distribution is bimodal with varying weights of the two modes

Simulating a dissipative Ising system • mean number kept constant by adjusting Rabi frequency • bimodality becomes more pronounced for longer excitation durations 20 µs

950 µs

Simulating a dissipative Ising system Detuning = 11.5 MHz

0

10

20

30

0

10

20

30

• on resonace (grey) the counting statistics goes from Poissonian to highly subPoissonian (negative Q-factor) • off resonance (blue) the variance is positive and peaks at half the maximum number

Simulating a dissipative Ising system

• the higher central moments reveal subtle details of the counting distribution, so they can be used to test model predictions with high accuracy

Simulating a dissipative Ising system • the Binder cumulant shows a characteristic dependence on the mean number both on resonance and off resonance • possibly useful for identifying phase transitions (finite size scaling)?

Simulating a dissipative Ising system

Towards a quantum simulator with cold Rydberg atoms creation and detection of Rydberg excitations in a cold cloud revealing strong Rydberg-Rydberg interactions through counting statistics using full counting statistics as a tool for gaining insight into the system using cold Rydberg atoms to simulate a dissipative Ising system

study dynamics finite size scaling move towards coherent regime ordered structures (optical lattice)

Towards a quantum simulator with cold Rydberg atoms creation and detection of Rydberg excitations in a cold cloud revealing strong Rydberg-Rydberg interactions through counting statistics using full counting statistics as a tool for gaining insight into the system using cold Rydberg atoms to simulate a dissipative Ising system

study dynamics finite size scaling move towards coherent regime ordered structures (optical lattice) C. Simonelli, Tesi di laurea, Pisa 2014