Hamiltonian engineering via invariants and dynamical algebra

We use the dynamical algebra of a quantum system and its dynamical invariants to inverse engineer feasible Hamiltonians for implementing shortcuts to adiabaticity. These are speeded up processes that end up with the same populations as slow, adiabatic ones. As application examples, we design families of shortcut Hamiltonians that drive two- and three-level systems between initial and final configurations, imposing physically motivated constraints on the terms (generators) allowed in the Hamiltonian.We are grateful to K. Takahashi and R. Kosloff for stimulating discussions. We acknowledge funding by Grants No. IT472-10 and No. FIS2009-12773-C02-01, and theUPV/EHU Program No. UFI 11/55. E.T. is supported by the Basque Government postdoctoral program. S.M.-G. acknowledges support from a UPV/EHU fellowship.Publicad

Shortcuts to adiabaticity: Fast-forward approach

The "fast-forward"approach by Masuda and Nakamura generates driving potentials to accelerate slow quantum adiabatic dynamics. First we present a streamlined version of the formalism that produces the main results in a few steps. Then we show the connection between this approach and inverse engineering based on Lewis-Riesenfeld invariants. We identify in this manner applications in which the engineered potential does not depend on the initial state. Finally we discuss more general applications exemplified by wave splitting processes.We are grateful to S. Masuda and K. Nakamura for discussing their method; also to G. Labeyrie for comments on experimental techniques. We acknowledge funding by Projects No. GIU07/40 and No. FIS2009-12773-C02-01, and the UPV/EHU under program UFI 11/55. E.T. acknowledges financial support from the Basque Government (Grant No.BFI08.151)

Fast transport of two ions in an anharmonic trap

We design fast trajectories of a trap to transport two ions using a shortcut-to-adiabaticity technique based on invariants. The effects of anharmonicity are analyzed first perturbatively, with an approximate, single relative-motion mode, description. Then, we use classical calculations and full quantum calculations. This allows us to identify discrete transport times that minimize excitation in the presence of anharmonicity. An even better strategy to suppress the effects of anharmonicity in a continuous range of transport times is to modify the trajectory using an effective trap frequency shifted with respect to the actual frequency by the coupling between relative and center-of-mass motions.We are grateful to A. Ruschhaupt, D. Leibfried, and U. Poschinger for useful comments. We acknowledge funding by Grants No. IT472-10 and No. FIS2009-12773-C02-01, and the UPV/EHU Program UFI 11/55. M.P. acknowledges a fellowship by UPV/EHU

Noise resistant quantum control using dynamical invariants

A systematic approach to design robust control protocols against the influence of different types of noise is introduced. We present control schemes which protect the decay of the populations avoiding dissipation in the adiabatic and nonadiabatic regimes and minimize the effect of dephasing. The effectiveness of the protocols is demonstrated in two different systems. Firstly, we present the case of population inversion of a two-level system in the presence of either one or two simultaneous noise sources. Secondly, we present an example of the expansion of coherent and thermal states in harmonic traps, subject to noise arising from monitoring and modulation of the control, respectively.We acknowledge L McCaslin for fruitful discussions, funding by the Israeli Science Foundation, the US Army Research Office under Contract W911NF- 15-1-0250, the Basque Government (Grant No. IT986-16), MINECO/FEDER,UE (Grants No. FIS2015-70856-P and No. FIS2015-67161-P), and QUITEMAD+CM S2013-ICE2801

Invariant-based inverse engineering of time-dependent, coupled harmonic oscillators

Two-dimensional (2D) systems with time-dependent controls admit a quadratic Hamiltonian modeling near potential minima. Independent, dynamical normal modes facilitate inverse Hamiltonian engineering to control the system dynamics, but some systems are not separable into independent modes by a point transformation. For these "coupled systems" 2D invariants may still guide the Hamiltonian design. The theory to perform the inversion and two application examples are provided: (i) We control the deflection of wave packets in transversally harmonic wave guides and (ii) we design the state transfer from one coupled oscillator to another.This work was supported by the Basque Country Government (Grant No. IT986-16), and by PGC2018-101355-B-I00 (MCIU/AEI/FEDER,UE). E.T. acknowledges support from PGC2018-094792-B-I00 (MCIU/AEI/FEDER,UE), CSIC Research Platform PTI-001, and CAM/FEDER No. S2018/TCS-4342 (QUITEMAD-CM)

Single-atom heat engine as a sensitive thermal probe

We propose employing a quantum heat engine as a sensitive probe for thermal baths. In particular, we study a single-atom Otto engine operating in an open thermodynamic cycle. Owing to its cyclic nature, the engine is capable of translating small temperature differences between two baths into a macroscopic oscillation in a flywheel. We present analytical and numerical modeling of the quantum dynamics of the engine and estimate it to be capable of detecting temperature differences as small as 2 muK. This sensitivity can be further improved by utilizing quantum resources such as squeezing of the ion motion. The proposed scheme does not require quantum state initialization and is able to detect small temperature differences in a wide range of base temperatures.We thank Samuel T Dawkins, Daniel Basilewitsch and Daniel M Reich for valuable discussions. We acknowledge financial support from the German Science Foundation (DFG) under project Thermal Machines in the QuantumWorld (FOR2724). AL acknowledges support of the Photonics at Thermodynamic Limits Energy Frontier Research Center funded by the US Department of Energy, Office of Science and Office of Basic Energy Sciences under Award Number DE-SC0019140. ET acknowledges support from Project PGC2018-094792-B-I00 (MCIU/AEI/FEDER,UE), CSIC Research Platform PTI-001 and CAM/FEDER Project No. S2018/TCS-4342 (QUITEMAD-CM).Publicad

Fast transitionless expansions of cold atoms in optical Gaussian-beam traps

We study fast expansions of cold atoms in a three-dimensional Gaussian-beam optical trap. Three different methods to avoid final motional excitation are compared: inverse engineering using Lewis-Riesenfeld invariants, which provides the best overall performance, a bang-bang approach, and a fast adiabatic approach. We analyze the excitation effect of anharmonic terms, radial-longitudinal coupling, and radial-frequency mismatch. In the inverse-engineering approach these perturbations can be suppressed or mitigated by increasing the laser beam waist.We thank G. C. Hegerfeldt for useful discussions. We acknowledge funding by the Basque government (Grant No. IT472-10), Ministerio de Ciencia e Innovación (Grant No. FIS2009-12773-C02-01), and the UPV/EHU under program UFI 11/55. X.C. thanks the Juan de la Cierva Programme, the National Natural Science Foundation of China (Grants No. 60806041 and No. 61176118), and the Shanghai Leading Academic Discipline Program (Grant No. S30105); E.T. thanks the Basque government (Grant No. BFI08.151); and D.G.O. thanks the Agence National de la Recherche, the Région Midi-Pyrénées, University Paul Sabatier (OMASYC project), and the Institut Universitaire de France

Invariant-Based Inverse Engineering of Crane Control Parameters

By applying invariant-based inverse engineering in the small-oscillation regime, we design the time dependence of the control parameters of an overhead crane (trolley displacement and rope length) to transport a load between two positions at different heights with minimal final-energy excitation for a microcanonical ensemble of initial conditions. The analogy between ion transport in multisegmented traps or neutral-atom transport in moving optical lattices and load manipulation by cranes opens a route for a useful transfer of techniques among very different fields.We acknowledge our discussions with S. Martínez-Garaot and M. Palmero. This work was supported by Eusko Jaurlaritza (Grant No. IT986-16); MINECO/ FEDER,UE (Grants No. FIS2015-67161-P and No. FIS2015-70856-P); QUITEMAD+CM S2013- ICE2801; and by Programme Investissements d'Avenir under the program ANR-11-IDEX 0002-02, reference ANR-10-LABX-0037-NEXT

Vibrational Mode Multiplexing of Ultracold Atoms

Sending multiple messages on qubits encoded in different vibrational modes of cold atoms or ions along a transmission waveguide requires us 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.This work was supported by the National Natural Science Foundation of China (Grant No. 61176118), Grants No. 12QH1400800 IT472-10, No. BFI-2010-255, No. 13PJ1403000, No. FIS2012-36673-C03-01, and the program UFI 11/55. S. M.-G. acknowledges support from a fellowship from UPV/EHU

Ultraviolet laser pulses with multigigahertz repetition rate and multiwatt average power for fast trapped-ion entanglement operations

The conventional approach to perform two-qubit gate operations in trapped ions relies on exciting the ions on motional sidebands with laser light, which is an inherently slow process. One way to implement a fast entangling gate protocol requires a suitable pulsed laser to increase the gate speed by orders of magnitude. However, the realization of such a fast entangling gate operation presents a big technical challenge, as such the required laser source is not available off-the-shelf. For this, we have engineered an ultrafast entangling gate source based on a frequency comb. The source generates bursts of several hundred mode-locked pulses with pulse energy ∼800 pJ at 5 GHz repetition rate at 393.3 nm and complies with all requirements for implementing a fast two-qubit gate operation. Using a single, chirped ultraviolet pulse, we demonstrate a rapid adiabatic passage in a Ca+ ion. To verify the applicability and projected performance of the laser system for inducing entangling gates we run simulations based on our source parameters. The gate time can be faster than a trap period with an error approaching 10−4