A protocol is discussed for preparing a spin chain in a generic many-body state in the asymptotic limit of tailored non-unitary dynamics. The dynamics require the spectral resolution of the target state, optimized coherent pulses, engineered dissipat
ion, and feedback. As an example, we discuss the preparation of an entangled antiferromagnetic state, and argue that the procedure can be applied to chains of trapped ions or Rydberg atoms.
A quasi one--dimensional system of trapped, repulsively interacting atoms (e.g., an ion chain) exhibits a structural phase transition from a linear chain to a zigzag structure, tuned by reducing the transverse trap potential or increasing the particl
e density. Since it is a one dimensional transition, it takes place at zero temperature and therefore quantum fluctuations dominate. In [Fishman, et al., Phys. Rev. B 77, 064111 (2008)] it was shown that the system close to the linear-zigzag instability is described by a $phi^4$ model. We propose a mapping of the $phi^4$ field theory to the well known Ising chain in a transverse field, which exhibits a quantum critical point. Based on this mapping, we estimate the quantum critical point in terms of the system parameters. This estimate gives the critical value of the transverse trap frequency for which the quantum phase transition occurs, and which has a finite, measurable deviation from the critical point evaluated within the classical theory. A measurement is suggested for atomic systems which can probe the critical trap frequency at sufficiently low temperatures T. We focus in particular on a trapped ion system, and estimate the implied limitations on T and on the interparticle distance. We conclude that the experimental observation of the quantum critical behavior is in principle accessible.
The efficiency of extracting single atoms or molecules from an ultracold bosonic reservoir is theoretically investigated for a protocol based on lasers, coupling the hyperfine state in which the atoms form a condensate to another stable state, in whi
ch the atom experiences a tight potential in the regime of collisional blockade, the quantum tweezers. The transfer efficiency into the single-atom ground state of the tight trap is fundamentally limited by the collective modes of the condensate, which are thermally and dynamically excited. The noise due to these excitations can be quenched for sufficiently long laser pulses, thereby achieving high efficiencies. These results show that this protocol can be applied for initializing a quantum register based on tweezer traps for neutral atoms.
A string of trapped ions at zero temperature exhibits a structural phase transition to a zigzag structure, tuned by reducing the transverse trap potential or the interparticle distance. The transition is driven by transverse, short wavelength vibrati
onal modes. We argue that this is a quantum phase transition, which can be experimentally realized and probed. Indeed, by means of a mapping to the Ising model in a transverse field, we estimate the quantum critical point in terms of the system parameters, and find a finite, measurable deviation from the critical point predicted by the classical theory. A measurement procedure is suggested which can probe the effects of quantum fluctuations at criticality. These results can be extended to describe the transverse instability of ultracold polar molecules in a one dimensional optical lattice.
Cold atoms, driven by a laser and simultaneously coupled to the quantum field of an optical resonator, can self-organize in periodic structures. These structures are supported by the optical lattice, which emerges from the laser light they scatter in
to the cavity mode, and form when the laser intensity exceeds a threshold value. We study theoretically the quantum ground state of these structures above the pump threshold of self-organization, by mapping the atomic dynamics of the self-organized crystal to a Bose-Hubbard model. We find that the quantum ground state of the self-organized structure can be the one of a Mott-insulator or a superfluid, depending on the pump strength of the driving laser. For very large pump strengths, where the intracavity intensity is maximum and one would expect a Mott-insulator state, we find intervals of parameters where the system is superfluid. These states could be realized in existing experimental setups.
