Shaken not stirred: creating exotic angular momentum states by shaking an optical lattice

Abstract

We propose a method to create higher orbital states of ultracold atoms in the Mott regime of an optical lattice. This is done by periodically modulating the position of the trap minima (known as shaking) and controlling the interference term of the lasers creating the lattice. These methods are combined with techniques of shortcuts to adiabaticity. As an example of this, we show specifically how to create an anti-ferromagnetic type ordering of angular momentum states of atoms. The specific pulse sequences are designed using Lewis-Riesenfeld invariants and a fourlevel model for each well. The results are compared with numerical simulations of the full Schrödinger equation. arXiv:1603.05927v1 [quant-ph]

Noise resistant quantum control using dynamical invariants

“…STA are control methods to derive protocols which reach fidelities of slow adiabatic processes in significantly shorter times. STA have been applied in a wide variety of fields including quantum computation [11][12][13][14], cooling [5,15], quantum transport [16,17], quantum state preparation [18][19][20][21], cold atoms manipulation [22][23][24][25][26][27][28], many-body state engineering [29][30][31][32] and polyatomic molecules control [33], design of optical devices [34,35] and linear chains [36], or mechanical engineering [37,38].…”

Selective population of a large-angular-momentum state in an optical lattice

“…More specifically, the amplitude modulation presented here can create two excitations in a given spatial direction. The position modulation (or shaking) outlined in [41] can create one excitation in a given spatial direction. In both cases, the part of the wavefunctions in the orthogonal direction must have the same parity for the coupling to be non-zero.…”

“…Analogous to [41], we make a four-level approximation assuming that it is sufficient to considerer only the four most relevant eigenstates of H 0 localized in the central site. Different from [41], these four eigenstates are now {|00 , |20 , |02 , |22 } (see Fig.…”

“…Analogous to [41], we make a four-level approximation assuming that it is sufficient to considerer only the four most relevant eigenstates of H 0 localized in the central site. Different from [41], these four eigenstates are now {|00 , |20 , |02 , |22 } (see Fig. 2); in coordinate representation, these four basis states are given by r|ij = Γ i (x)Γ j (y), where Γ 0 (x) and Γ 2 (x) are, respectively, the localized ground and second excited states of a one-dimensional unperturbed optical lattice site.…”

“…3. In this paper, we consider a different physical operation, namely amplitude modulation, than the shaking examined in [41]. This leads to a different driving Hamiltonian H 1 (t).…”