Vibrational Mode Multiplexing of Ultracold Atoms

Abstract

Sending multiple messages on qubits encoded in different vibrational modes of cold atoms or ions along a transmission waveguide requires to merge first and then separate the modes at input and output ends. Similarly, different qubits can be stored in the modes of a trap and be separated later. We design the fast splitting of a harmonic trap into an asymmetric double well so that the initial ground vibrational state becomes the ground state of one of two final wells, and the initial first excited state becomes the ground state of the other well. This might be done adiabatically by slowly deforming the trap. We speed up the process by inverse engineering a double-function trap using dynamical invariants. The separation (demultiplexing) followed by an inversion of the asymmetric bias and then by the reverse process (multiplexing) provides a population inversion protocol based solely on trap reshaping. Introduction.-One of the main goals of atomic physics is to achieve an exhaustive control of atomic states and dynamics [1]. The ultra-cold domain is particularly suitable for this aim as it provides a rich scenario of quantum states and phenomena. Atom optics and atomtronics [2] intend to manipulate cold atoms in circuits and devices for applications in metrology, quantum information, or fundamental science. These devices are frequently inspired by electronics (e.g. the atom diode [3,4], the transistor [2], atom chips [5]), or optics (e.g. beam splitters [6], or multiplexing [7,8]).In this paper we shall focus on a cold-atom realization of multiplexing, a basic process in modern telecommunications. Multiplexing is the transmission of different messages via a single physical medium. A multiplexer combines signals from several emitters into a single medium whereas a demultiplexer performs the reverse operation. The concept of multiplexing is relevant for quantum information processing (for its use in quantum repeaters see [9,10], or for trapped ions [11]). We envision here optical or magnetic waveguides for atoms holding several transverse orthogonal modes [12][13][14][15]. If the qubit is encoded in the internal state of the atom, several qubits may be carried out simultaneously by different modes. To develop such a quantum-information architecture, fast mul-

Fast driving between arbitrary states of a quantum particle by trap deformation

“…Furthermore, this protocol may also be used to create higher Fock states just by changing the final states. Open questions left for future work include comparing the present protocol with other methods that break the parity symmetry of the potential without using the fast-forward approach [7], or optimizing the robustness versus noise and perturbations [6]. Applications of the method go beyond quantum mechanics, e.g.…”

“…The connection between states with different topological properties is of much interest for quantum computing processes because it allows, for example, to prepare Fock states by deforming the trap without using laser excitation of internal states [7]. Using sequences of π-pulses is demanding, as a N -phonon Fock state needs very precise N pulses, but fluctuations in intensity, frequency, and timing imperfections give a reduced fidelity [32].…”

“…Such trap shaping on a short timescale has been proven useful, for example, to implement quantum thermodynamical cycles [20,21], or to implement a scalable architecture for quantum information processing [22]. It is also important for some quantum information processing schemes such as multiplexing and demultiplexing when information is encoded in external degrees of freedom [7], for Fock state creation [23], or velocity control [24,25], and it is expected to become more and more relevant given the current interest to develop quantum technologies. * Electronic address: sofia.martinez@ehu.eus…”

“…In this context, a few methods that bypass adiabatic transformations by designing appropriate time-dependent Hamiltonians have been set up. This includes methods based on exact solutions with time-dependent scaling parameters [2][3][4][5], methods based on dynamical Lewis-Riesenfeld invariants [3,6,7], the transitionless tracking algorythm that adds counteradiabatic terms to the Hamiltonian [8,9], the fast-forward approach [10][11][12][13], Lie-algebraic methods [14,15], or the fast quasi-adiabatic approach [16].…”

Shortcut to adiabaticity in a Stern-Gerlach apparatus

“…These methods enable one to guarantee a transitionless evolution faster than the time scale imposed by the adiabatic regime. The STA approach has been shown experimentally to efficently speed up the transport or manipulation of wave functions [10][11][12][13][14][15][16][17] and even thermodynamical transformations [18][19][20]. Concerning the transfer of quantum states, recent impressive implementations have been reported in cold atoms experiments [21], solid-state architectures [22] or in optomechanical systems [23].…”