# Momentum Group

## Contents

Peter Domokos won the Momentum Prize in 2011. This grant supports the research on **‘Quantum measurement in hybrid mesoscopic systems and networks’** for the period 2011–2015.

## Overall project objectives

By the end of the last century, laser physics and the technology of quantum optics has been developed to the level which allows for the controlled manipulation of quantum objects, such as photons, ions and atoms, in all their relevant degrees of freedom at the ultimate quantum noise limit. The next challenge of atomic and quantum optics research comprises the extension of coherent quantum manipulation to composite objects, such as larger molecules or networks of elementary systems. This attempt makes it necessary to explore the mesoscopic domain between classical and quantum worlds (macroscopic and microscopic sizes) in which quantum measurement theory is not understood. The project aims at studying such fundamental questions of quantum theory in relation to experimentally investigated mesoscopic systems.

## Ultracold atoms in optical resonators

### Research objectives

- simulation of artificial, long-range interactions
- supersolidity
- quantum phase transitions in non-equilibrium systems

Schematic plot of a Bose-Einstein condensate (BEC) interacting with a single mode optical cavity. The cavity mode is described by a cos(*kx*) function along the cavity axis while it has a Gaussian envelope in the transverse direction. The BEC wave function evolves dynamically in time due to the interaction with the radiation field. The figure illustrates self-organization. A quasi homogeneous BEC (which has a shape of an elongated ellipsoid with its semi major axis well exceeding the optical wavelength) is illuminated by a pumping laser perpendicular to the cavity axis. When the intensity of the pump laser is below a threshold value (left panel) the BEC wave function remains homogeneous and incapable of scattering a classical field into the resonator. However, above threshold intensity (right panel) the BEC self-organizes into a one-wavelength pattern that scatters photons constructively into the resonator and thus stabilizes the optical potential supporting the Bragg lattice.

### Participants

Peter Domokos

(group leader)

Dávid Nagy

(postdoc)

Gergely Szirmai

(postdoc)

András Vukics

(postdoc)

Gábor Kónya

(PhD student)

### Collaborators

- Prof. Helmut Ritsch, Universität Innsbruck
- Prof. Tilman Esslinger, ETH Zürich

### References

- D. Nagy, G. Szirmai, and P. Domokos: Critical exponent of a quantum-noise-driven phase transition: The open-system Dicke model, Phys. Rev. A
**84**, 043637 (2011) - D. Nagy, G. Konya, G. Szirmai, and P. Domokos: Dicke-Model Phase Transition in the Quantum Motion of a Bose-Einstein Condensate in an Optical Cavity, Phys. Rev. Lett.
**104**, 130401 (2010)

## Interfacing carbon nanotubes and Bose-Einstein condensates of atoms

### Research objectives

- interfacing different kinds of degrees of freedom (electronic, spin, motional, etc.)
- controlled mesoscopic transport
- ultracold atoms as a tool for quantum measurement

Quantum galvanometer on an atom chip. A BEC is loaded into the magnetic microtrap created by classical electric currents through integrated conductors on a dielectric substrate (represented on the bottom of the chip). A suspended carbon nanotube (CNT) is also part of the electric circuit and transports the quantum current. The mechanically oscillating CNT creates a magnetic field inducing hyperfine transitions in the atoms. Atoms thus transferred to untrapped states are detected by single-atom detector.

### Participants

Peter Domokos

(group leader)

Tamás Kiss

(senior scientist)

Orsolya Kálmán

(postdoc)

Zoltán Kurucz

(postdoc)

Zoltán Darázs

(PhD student)

András Dombi

(PhD student)

### Collaborators

- Prof. József Fortágh, Universitat Tübingen

### References

- O. Kálmán, T. Kiss, J. Fortágh, and P. Domokos: Quantum Galvanometer by Interfacing a Vibrating Nanowire and Cold Atoms, Nano Lett., 2012,
**12**, 435–439 (2012)

## Quantum networks

### Research objectives

- quantum walk
- modeling topological insulators
- measurement back-action induced complex chaos

Schematic representation of one iteration step of the entanglement purification process. The diamond shaped elements denote acceptance of the pair of qubits only when both measurements yield 0. The depicted procedure is used to prepare from an ensemble *E′* made up of pairs of qubits all in a state |*ψ*⟩, an ensemble *E* made made up of pairs of qubits in the state |*ψ*′⟩. During the procedure, half of the pairs in *E* are completely used up, while a portion of the other half is retained depending on the measurement outcome. *H* is the Hadamard gate.

Convergence of given initial states to the two limiting cycles as a function of the complex parameter *ζ*. The blue color denotes convergence to a maximally entangled state, and the green color the convergence to the cycle of the two separable states.

### Participants

Tamás Kiss

(senior scientist)

János Asbóth

(postdoc)

Zoltán Darázs

(PhD student)

Bálint Kollár

(PhD student)

### Collaborators

- Prof. Igor Jex, Czech Technical University in Prague
- Prof. Oliver Mülken and Prof. Alexander Blumen, University of Freiburg

### References

- T. Kiss, S. Vymetal, L. D. Toth, A. Gabris, I. Jex, G. Alber: Measurement-Induced Chaos with Entangled States, Phys. Rev. Lett.
**107**, 100501 (2011)