The decoherence of nonclassical motional states of a trapped $^9 {\rm Be^+}$ ion in a recent experiment is investigated theoretically. Sources of decoherence considered here destroy the characteristic coherent quantum dynamics of the system but do not cause energy dissipation. Here they are first introduced phenomenologically and then described using a microscopic Hamiltonian formulation. Theoretical predictions are compared to experimental results.
We present an efficient scheme to generate two-mode SU(2) macroscopic quantum superposition (Schrödinger cat) states, entangled number states and entangled coherent states for the vibrational motion of an ion trapped in a two-dimensional harmonic potential well. We also show that the same scheme can be used to realize a Fredkin gate operation.
Nonclassical motional states of matter are of interest both from a fundamental perspective but also for their potential technological applications as resources in various quantum processing tasks such as quantum teleportation, sensing, communication, and computation. In this work we explore the motional effects of a harmonically trapped, excited two-level emitter coupled to a one-dimensional (1D) photonic system. As the emitter decays it experiences a momentum recoil that entangles its motion with the emitted photon pulse. In the long-time limit the emitter relaxes to its electronic ground sta…
We propose to synthesize arbitrary nonclassical motional states in optomechanical systems by using sideband excitations and photon blockade. We first demonstrate that the Hamiltonian of the optomechanical systems can be reduced, in the strong single-photon optomechanical coupling regime when the photon blockade occurs, to one describing the interaction between a driven two-level trapped ion and the vibrating modes, and then show a method to generate target states by using a series of classical pulses with desired frequencies, phases, and durations. We further analyze the effect of the photon l…
We investigate nonclassical properties of the output of a Bose-Einstein condensate in Milburn's model of intrinsic decoherence. It is shown that the squeezing property of the atom laser is suppressed due to decoherence. Nevertheless, if some very special conditions were satisfied, the squeezing properties of atom laser could be robust against the decoherence.
We make a comparative study of quadrature squeezing, photon-number distribution and Wigner function in a decayed quantum system. Specifically, for a field mode prepared initially in cat states interacting with a zero-temperature environment, we show that the rate of reduction of the nonclassical effects in this system is proportional to the occurrence of the decoherence process.
In this thesis concrete quantum systems are investigated in the framework of the environment induced decoherence. The focus is on the dynamics of highly nonclassical quantum states, the Wigner function of which are negative over some regions of their domains. One of the chosen physical systems is a diatomic molecule, where the potential energy of the nuclei is an anharmonic function of their distance. A system of two-level atoms, which can be important from the viewpoint of quantum information technology, is also investigated. A method is described that is valid in both systems and can determi…
The reduced dynamics of an atomic qubit coupled both to its own quantized center of mass motion through the spatial mode functions of the electromagnetic field, as well as the vacuum modes, is calculated in the influence functional formalism. The formalism chosen can describe the entangled non-Markovian evolution of the system with a full account of the coherent back-action of the environment on the qubit. We find a slight increase in the decoherence due to the quantized center of mass motion and give a condition on the mass and qubit resonant frequency for which the effect is important. In op…
We introduce Hermite polynomial excitation squeezed vacuum (SV) H_{n}(O)S(r)|0> with O=u a+v a^{+}. We investigate analytically the nonclassical properties according to Mandel's Q parameter, second correlation function, squeezing effect and the negativity of Wigner function (WF). It is found that all these nonclassicalities can be enhanced by H_{n}(O)operation and adjustable parameters u and v. In particular, the optimal negative volume delta_{opt}of WF can be achieved by modulating u and v for n>=2,while delta is kept unchanged for n=1. Furthermore, the decoherence effect of phase-sensitive e…
The dominant error sources for state-of-the-art laser-free trapped-ion entangling gates are decoherence of the qubit state and the ion motion. The effect of these decoherence mechanisms can be suppressed with additional control fields, or with techniques that have the disadvantage of reducing gate speed. Here, we propose using a near-motional-frequency magnetic field gradient to implement a laser-free gate that is simultaneously resilient to both types of decoherence, does not require additional control fields, and has a relatively small cost in gate speed.
We measure and characterize anomalous motional decoherence of an atomic ion confined in the lowest quantum levels of a novel rf ion trap that features moveable electrodes. The scaling of decoherence rate with electrode proximity is measured, and when the electrodes are cooled from 300 K to 150 K, the decoherence rate is suppressed by an order of magnitude. This provides direct evidence that anomalous motional decoherence of trapped ions stems from microscopic noisy potentials on the electrodes. These observations are relevant to quantum information processing schemes using trapped ions or othe…
We demonstrate long-lived coherence in internal hyperfine states of a single \Ca{43} trapped-ion qubit $[T_2=1.2(2)\s]$, and in external motional states of a single \Ca{40} trapped-ion qubit $[T_2'=0.18(4)\s]$, in the same apparatus. The motional decoherence rate is consistent with the heating rate, which was measured to be 3(1) quanta/sec. Long coherence times in the external motional states are essential for performing high-fidelity quantum logic gates between trapped-ion qubits. The internal-state $T_2$ time that we observe in \Ca{43}, which has not previously been used as a trapped-ion qub…
A quantum memory interacts with its environment and loses information via decoherence as well as incoherence. A robust quantum control that prepares, preserves, and manipulates nonclassical correlations even in the presence of environmental influence is of paramount importance in quantum information processing. A well-known technique to suppress decoherence, namely Dynamical Decoupling (DD), consists of a sequence of rapid flips applied to the system in order to refocus the system-environment interactions. In this work, we integrate DD with quantum gates using optimal control techniques to rea…
We study dynamics of nonclassical correlations by exactly solving a model consisting of two atomic qubits with spontaneous emission. We find that the nonclassical correlations defined by different measures give different qualitative characterizations of those correlations. The relative behaviors of those correlation measures are presented explicitly for various quantum states in the two-qubit atomic system. In particular, we find that the robustness of quantum correlations can be greatly enhanced by performing appropriate local unitary operations on the initial state of the system.
We prepare a superposition of two motional states by addressing lithium atoms immersed in a Bose-Einstein condensate of sodium with a species-selective potential. The evolution of the superposition state is characterized by the populations of the constituent states as well as their coherence. The latter we extract employing a novel scheme analogous to the spin-echo technique. Comparing the results directly to measurements on freely-evolving fermions allows us to isolate the decoherence effects induced by the bath. In our system, the decoherence time is close to the maximal possible value since…
We examine the dynamics of a qubit stored in the motional degrees of freedom of an ultra-cold ion in an ion trap which is subject to the decoherence effects of a finite-temperature bath. We discover an encoding of the qubit, in two of the motional modes of the ion, which is stable against the occurrence of either none or one quantum jump. For the case of a zero-temperature bath we describe how to transfer only the information concerning the occurrence of quantum jumps and their types to a measuring apparatus, without affecting the ion's motional state significantly. We then describe how to gen…
We investigate theoretical decoherence effects of the motional degrees of freedom of a single trapped atomic/ionic electronically coded qubit. For single bit rotations from a resonant running wave laser field excitation, we found the achievable fidelity to be determined by a single parameter characterized by the motional states. Our quantitative results provide a useful realistic view for current experimental efforts in quantum information and computing.
Favored schemes for trapped-ion quantum logic gates use bichromatic laser fields to couple internal qubit states with external motion through a "spin-dependent force." We introduce a new degree of freedom in this coupling that reduces its sensitivity to phase decoherence. We demonstrate bichromatic spin-dependent forces on a single trapped $^{111}$Cd$^+$ ion, and show that phase coherence of the resulting "Schrödinger-cat" states of motion depends critically upon the spectral arrangement of the optical fields. This applies directly to the operation of entangling gates on multiple ions.
A method for gaining information about the phonon-number moments and the generalized nonlinear and linear quadratures in the motion of trapped ions (in particular, position and momentum) is proposed, valid inside and outside the Lamb-Dicke regime. It is based on the measurement of first time derivatives of electronic populations, evaluated at the motion-probe interaction time t=0. In contrast to other state-reconstruction proposals, based on measuring Rabi oscillations or dispersive interactions, the present scheme can be performed resonantly at infinitesimal short motion-probe interaction tim…
We present a nonlinear decoherence model which models decoherence effect caused by various decohereing sources in a quantum system through a nonlinear coupling between the system and its environment, and apply it to investigating decoherence in nonclassical motional states of a single trapped ion. We obtain an exactly analytic solution of the model and find very good agreement with experimental results for the population decay rate of a single trapped ion observed in the NIST experiments by Meekhof and coworkers (D. M. Meekhof, {\it et al.}, Phys. Rev. Lett. {\bf 76}, 1796 (1996)).
We propose the implementation of selective interactions of atom-motion subspaces in trapped ions. These interactions yield resonant exchange of population inside a selected subspace, leaving the others in a highly dispersive regime. Selectivity allows us to generate motional Fock (and other nonclassical) states with high purity out of a wide class of initial states, and becomes an unconventional cooling mechanism when the ground state is chosen. Individual population of number states can be distinctively measured, as well as the motional Wigner function. Furthermore, a protocol for implementin…
Maximizing Nonclassicality of Massive Objects via Quantum Zeno Effect
Shiv Nadar Institution of Eminence（希夫纳达尔卓越学院）；S. N. Bose National Centre for Basic Sciences（S.N. 玻色基础科学国家中心）；Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学与物理学院）；School of Physics and Astronomy, University of Southampton（南安普顿大学物理与天文学院）；Raman Research Institute (RRI)（拉曼研究所）；Bose Institute（玻色研究所）；Department of Physics and Astronomy, University College London（伦敦大学学院物理与天文学系）
In quantum interaction problems with explicitly time-dependent interaction Hamiltonians, the time ordering plays a crucial role for describing the quantum evolution of the system under consideration. In such complex scenarios, exact solutions of the dynamics are rarely available. Here we study the nonlinear vibronic dynamics of a trapped ion, driven in the resolved sideband regime with some small frequency mismatch. By describing the pump field in a quantized manner, we are able to derive exact solutions for the dynamics of the system. This eventually allows us to provide analytical solutions …
Following a recent proposal of L. Wang and D. Babikov, J. Chem. Phys. 137, 064301 (2012), we theoretically illustrate the possibility of using the motional states of a $Cd^+$ ion trapped in a slightly anharmonic potential to simulate the single-particle time-dependent Schrödinger equation. The simulated wave packet is discretized on a spatial grid and the grid points are mapped on the ion motional states which define the qubit network. The localization probability at each grid point is obtained from the population in the corresponding motional state. The quantum gate is the elementary evolutio…
A single Ca+ ion in a Paul trap has been cooled to the ground state of vibration with up to 99.9% probability. Starting from this Fock state |n=0> we have demonstrated coherent quantum state manipulation on an optical transition. Up to 30 Rabi oscillations within 1.4 ms have been observed. We find a similar number of Rabi oscillations after preparation of the ion in the |n=1> Fock state. The coherence of optical state manipulation is only limited by laser and ambient magnetic field fluctuations. Motional heating has been measured to be as low as one vibrational quantum in 190 ms.
The measurement process is taken into account in the dynamics of trapped ions prepared in nonclassical motional states. The induced decoherence is shown to manifest itself both in the inhibition of the internal population dynamics and in a damping of the vibrational motion without classical counterpart. Quantitative comparison with present experimental capabilities is discussed, leading to a proposal for the verification of the predicted effects.
The generation of nonclassical states of a radiation field has become increasingly important in the past years given its various applications in quantum communication. The feasibility of generating such nonclassical states has been established in several branches of physics such as cavity electrodynamics, trapped ions, quantum dots, atoms inside cavities and so on. In this sense, we will discuss the issue of the generation of nonclassical states in the context of a superconducting qubit in a microcavity. It has been recently proposed a way to engineer quantum states using a SQUID charge qubit …
We demonstrate quantum control techniques for a single trapped ion in a cryogenic, surface-electrode trap. A narrow optical transition of Sr+ along with the ground and first excited motional states of the harmonic trapping potential form a two-qubit system. The optical qubit transition is susceptible to magnetic field fluctuations, which we stabilize with a simple and compact method using superconducting rings. Decoherence of the motional qubit is suppressed by the cryogenic environment. AC Stark shift correction is accomplished by controlling the laser phase in the pulse sequencer, eliminatin…
Interfacing ion qubits in separate traps is among the challenges towards scaling up ion quantum computing. This theoretical study focuses on using a conducting wire to couple the motional quantum states of ions in separate planar traps. This approach of interfacing ion traps provides an alternative to coupling distant qubits with lasers. We include the effects of $1/f^{\tildeα}$ (Anomalous) surface heating noise, using aggregate and recent experimental findings as the basis for an analytical model of the motional state decoherence time $t_{\mathrm{deco.}}$. Our optimized design for the couplin…
The Lindblad approach to open quantum systems is introduced for studying the dynamics of a single trapped ion prepared in nonclassical motional states and subjected to continuous measurement of its internal population. This results in an inhibition of the dynamics similar to the one occurring in the quantum Zeno effect. In particular, modifications to the Jaynes-Cummings collapses and revivals arising from an initial coherent state of motion in various regimes of interaction with the driving laser are dealt in detail.
We report on the immersion of a spin-qubit encoded in a single trapped ion into a spin-polarized neutral atom environment, which possesses both continuous (motional) and discrete (spin) degrees of freedom. The environment offers the possibility of a precise microscopic description, which allows us to understand dynamics and decoherence from first principles. We observe the spin dynamics of the qubit and measure the decoherence times (T1 and T2), which are determined by the spin-exchange interaction as well as by an unexpectedly strong spin-nonconserving coupling mechanism.
We investigate single ions of $^{40}Ca^+$ in Paul traps for quantum information processing. Superpositions of the S$_{1/2}$ electronic ground state and the metastable D$_{5/2}$ state are used to implement a qubit. Laser light on the S$_{1/2} \leftrightarrow$ D$_{5/2}$ transition is used for the manipulation of the ion's quantum state. We apply sideband cooling to the ion and reach the ground state of vibration with up to 99.9% probability. Starting from this Fock state $|n=0>$, we demonstrate coherent quantum state manipulation. A large number of Rabi oscillations and a ms-coherence time is ob…
We propose a scalable procedure to generate entangled superpositions of motional coherent states and electronic states in N trapped ions. Beyond their fundamental importance, these states may be of interest for quantum information processing and may be used in experimental studies of decoherence.
There are several known schemes for entangling trapped ion quantum bits for large-scale quantum computation. Most are based on an interaction between the ions and external optical fields, coupling internal qubit states of trapped-ions to their Coulomb-coupled motion. In this paper, we examine the sensitivity of these motional gate schemes to phase fluctuations introduced through noisy external control fields, and suggest techniques to suppress the resulting phase decoherence.
Qubits of long coherence time and fast quantum operations are long-sought objectives towards the realization of high-fidelity quantum operations and their applications to the quantum technologies. An electron levitated in a vacuum by a Paul trap is expected to be a good candidate, for its light mass and hence the high secular frequency which allows for the faster gate operations than those in trapped ions. Controlling the motional state of the trapped electron is a crucial issue, for it mediates an interaction between electron spins, intrinsic qubits embedded in electrons, and its decoherence …
We introduce a scheme to perform dissipation-assisted quantum information processing in ion traps considering realistic decoherence rates, for example, due to motional heating. By means of continuous sympathetic cooling, we overcome the trap heating, and show that the damped vibrational excitations can still be exploited to mediate coherent interactions as well as collective dissipative effects. We describe how to control their relative strength experimentally, allowing for protocols of coherent or dissipative generation of entanglement. This scheme can be scaled to larger ion registers for co…
Out-of-time-ordered correlators (OTOCs) have received considerable recent attention as qualitative witnesses of information scrambling in many-body quantum systems. Theoretical discussions of OTOCs typically focus on closed systems, raising the question of their suitability as scrambling witnesses in realistic open systems. We demonstrate empirically that the nonclassical negativity of the quasiprobability distribution (QPD) behind the OTOC is a more sensitive witness for scrambling than the OTOC itself. Nonclassical features of the QPD evolve with timescales that are robust with respect to de…
Continuous-variable (CV) encoding allows information to be processed compactly and efficiently on quantum processors. Recently developed techniques such as controlled beam-splitter operations and the near deterministic phonon subtractions make trapped ion systems attractive for exploring CV quantum computing. Here we propose a probabilistic scheme based on the boson sculpting technique for generating multipartite highly entangled states of motional modes of trapped ion systems. We also investigate the effects of decoherence on the fidelity of the generated state by performing numerical simulat…
We study heating of motional modes of a single ion and of extended ion crystals trapped in a linear radio frequency (rf) Paul trap with a precision of $Δ\dot{\bar{n}} \approx 0.2 $ phonons s$^{-1}$. Single-ion axial and radial heating rates are consistent and electric field noise has been stable over the course of four years. At a secular frequency of $ω_\mathrm{sec}=2π\times620$ kHz, we measure $\dot{\bar{n}} = 0.56(6)$ phonons s$^{-1}$ per ion for the center-of-mass (com) mode of linear chains of up to eleven ions and observe no significant heating of the out-of-phase (oop) modes. By displac…
We demonstrate sympathetic cooling of a 43Ca+ trapped-ion "memory" qubit by a 40Ca+ "coolant" ion near the ground state of both axial motional modes, whilst maintaining coherence of the qubit. This is an essential ingredient in trapped-ion quantum computers. The isotope shifts are sufficient to suppress decoherence and phase shifts of the memory qubit due to the cooling light which illuminates both ions. We measure the qubit coherence during 10 cycles of sideband cooling, finding a coherence loss of 3.3% per cooling cycle. The natural limit of the method is O(0.01%) infidelity per cooling cycl…
Oscillating magnetic fields and field gradients can be used to implement single-qubit rotations and entangling multi-qubit quantum gates for trapped-ion quantum information processing (QIP). With fields generated by currents in microfabricated surface-electrode traps, it should be possible to achieve gate speeds that are comparable to those of optically induced gates for realistic distances between the ion crystal and the electrode surface. Magnetic-field-mediated gates have the potential to significantly reduce the overhead in laser beam control and motional state initialization compared to c…
Interfacing quantum mechanics and gravity is one of the great open questions in natural science. Micromechanical oscillators have been suggested as a plausible platform to carry out these experiments. We present an experimental design aiming at these goals, inspired by Schmöle et al., Class. Quantum Grav. 33, 125031 (2016). Gold spheres weighing on the order a milligram will be positioned on large silicon nitride membranes, which are spaced at submillimeter distances from each other. These mass-loaded membranes are mechanical oscillators that vibrate at $\sim 2$ kHz frequencies in a drum mode.…
We demonstrate spectroscopy and thermometry of individual motional modes in a mesoscopic 2D ion array using entanglement-induced decoherence as a method of transduction. Our system is a $\sim$400 $μ$m-diameter planar crystal of several hundred $^9$Be$^+$ ions exhibiting complex drumhead modes in the confining potential of a Penning trap. Exploiting precise control over the $^9$Be$^+$ valence electron spins, we apply a homogeneous spin-dependent optical dipole force to excite arbitrary transverse modes with an effective wavelength approaching the interparticle spacing ($\sim$20 \nolinebreak$μ$m…
