We report the electromagnetically-induced-transparency (EIT) cooling of a large trapped $^{171}$Yb$^+$ ion chain to the quantum ground state. Unlike conventional EIT cooling, we engage a four-level tripod structure and achieve fast sub-Doppler cooling over all motional modes. We observe simultaneous ground-state cooling across the complete transverse mode spectrum of up to $40$ ions, occupying a bandwidth of over $3$ MHz. The cooling time is observed to be less than $300\,μ$s, independent of the number of ions. Such efficient cooling across the entire spectrum is essential for high-fidelity quantum operations using trapped ion crystals for quantum simulators or quantum computers.
We report the experimental observations on the simultaneous EIT effects for probe and trigger fields (double EIT) as well as the large cross-phase modulation (XPM) between the two fields in a four-level tripod EIT system of the D1 line of 87Rb atoms. The XPM coefficients (larger than 2*10-5cm2/W) and the accompanying transmissions (higher than 60%) are measured at slightly detuning of the probe field from the exact EIT resonance condition. The presented system can be applied in the recently proposed quantum information processing with weak cross-Kerr nonlinearities.
The electromagnetically induced transparency (EIT) phenomenon in a four level atomic system with tripod configuration is studied. The results show that this configuration is equivalent to the combination of two single three-level $Λ$ configurations, which, under certain conditions, results in the so-called double-EIT (DEIT) phenomenon. The properties of the double transparency windows for DEIT are discussed in detail and the possible experimental scheme is proposed.
We consider propagation of a probe pulse in an atomic medium characterized by a combined tripod and Lambda ($Λ$) atom-light coupling scheme. The scheme involves three atomic ground states coupled to two excited states by five light fields. It is demonstrated that dark states can be formed for such an atom-light coupling. This is essential for formation of the electromagnetically induced transparency (EIT) and slow light. In the limiting cases the scheme reduces to conventional $Λ$- or $N$-type atom-light couplings providing the EIT or absorption, respectively. Thus the atomic system can experi…
We investigate the problem of propagation of three-component resonant light pulses with adiabatically varying amplitudes through a medium consisting of atoms with the tripod level configuration. By means of both analytic and numerical methods we found the two modes of shape-preserving pulse propagation. The pulse propagation velocity is found to be either equal to the speed of light or significantly slowed down, depending on a particular propagation mode.
We discuss a laser cooling scheme for trapped atoms or ions which is based on double electromagnetically induced transparency (EIT) and makes use of a four-level atom in tripod configuration. The additional fourth atomic state is coupled by a strong coupling laser field to the usual three-level setup of single-EIT cooling. This effectively allows to create two EIT structures in the absorption spectrum of the system to be cooled, which may be controlled by the coupling laser field parameters to cancel both the carrier- and the blue-sideband excitations. In leading order of the Lamb-Dicke expans…
Electromagnetically-induced-transparency (EIT) cooling is a ground-state cooling technique for trapped particles. EIT offers a broader cooling range in frequency space compared to more established methods. In this work, we experimentally investigate EIT cooling in strings of trapped atomic ions. In strings of up to 18 ions, we demonstrate simultaneous ground state cooling of all radial modes in under 1 ms. This is a particularly important capability in view of emerging quantum simulation experiments with large numbers of trapped ions. Our analysis of the EIT cooling dynamics is based on a nove…
We present a general theory for laser-free entangling gates with trapped-ion hyperfine qubits, using either static or oscillating magnetic-field gradients combined with a pair of uniform microwave fields symmetrically detuned about the qubit frequency. By transforming into a `bichromatic' interaction picture, we show that either ${\hatσ_ϕ\otimes\hatσ_ϕ}$ or ${\hatσ_{z}\otimes\hatσ_{z}}$ geometric phase gates can be performed. The gate basis is determined by selecting the microwave detuning. The driving parameters can be tuned to provide intrinsic dynamical decoupling from qubit frequency fluct…
Systems of interacting classical harmonic oscillators have received considerable attention in the last years as analog models for describing electromagnetically induced transparency (EIT) and associated phenomena. We review these models and investigate their validity for a variety of physical systems using two- and three-coupled harmonic oscillators. From the simplest EIT-$Λ$ configuration and two-coupled single cavity modes we show that each atomic dipole-allowed transition and a single cavity mode can be represented by a damped harmonic oscillator. Thus, we have established a one-to-one corr…
A completely analytic description is given of the motion of a trapped ion which is in either an even or an odd coherent state. Comparison to recent theoretical and experimental work is made.
A completely analytic description is given of the motion of a trapped ion which is in either an even or an odd squeezed state. Comparison is made to recent results on the even or odd coherent states, and possible experimental work is discussed.
The process of exciting the gas of trapped bosons from an equilibrium initial state to strongly nonequilibrium states is described as a procedure of symmetry restoration caused by external perturbations. Initially, the trapped gas is cooled down to such low temperatures, when practically all atoms are in Bose-Einstein condensed state, which implies the broken global gauge symmetry. Excitations are realized either by imposing external alternating fields, modulating the trapping potential and shaking the cloud of trapped atoms, or it can be done by varying atomic interactions by means of Feshbac…
We theoretically propose and experimentally demonstrate a parallel-electromagnetically-induced transparency (parallel-EIT) cooling technique for ion crystals in the Paul trap. It has less stringent requirements on the cooling resonance condition than the standard electromagnetically-induced transparency (EIT) cooling, thus allowing, in principle, to simultaneously cool the motional mode spectrum with an arbitrary range. A proof-of-principle validation for this cooling scheme is experimentally demonstrated with up to 4 trapped 40Ca+ ions. We observe simultaneous near-ground-state cooling for al…
We study the quantum dynamics of an ion confined in a radiofrequency trap in interaction with either a Bose or spin-polarized Fermi gas. To this end, we derive quantum optical master equations in the limit of weak coupling and the Lamb-Dicke approximations. For the bosonic bath, we also include the so-called "Lamb-shift" correction to the ion trap due to the coupling to the quantum gas as well as the extended Fröhlich interaction within the Bogolyubov approximation that have been not considered in previous studies. We calculate the ion kinetic energy for various atom-ion scattering lengths as …
We propose a new scalable architecture for trapped ion quantum computing that combines optical tweezers delivering qubit state-dependent local potentials with oscillating electric fields. Since the electric field allows for long-range qubit-qubit interactions mediated by the center-of-mass motion of the ion crystal alone, it is inherently scalable to large ion crystals. Furthermore, our proposed scheme does not rely on either ground state cooling or the Lamb-Dicke approximation. We study the effects of imperfect cooling of the ion crystal, as well as the role of unwanted qubit-motion entanglem…
In this thesis, after a brief review of some concepts of Quantum Optics, we analyze a three-level atomic system in the conditions of electromagnetically induced transparency (EIT), and we investigate the propagation of a gaussian pulse along a cigar-shaped cloud of both cold and hot atoms in EIT regime. In particular, we show that it is possible to amplify a slow propagating pulse without population inversion. We also analyze the regime of anomalous light propagation showing that it is possible to observe superluminal energy propagation. In these conditions, it is possible to imprint reversibl…
We discuss the dynamical behavior of the entanglement between the internal and the external degrees of freedom of a trapped atom in electromagnetically-induced transparency (EIT) laser cooling. It is shown that essential features of the intricate entanglement dynamics observed in full numerical simulations of the underlying quantum master equation can be understood in terms of a two-state model on the basis of Landau-Zener splittings in the atom-laser field Hamiltonian. An extension of this model to an effective non-Hermitian Hamiltonian is constructed which describes the decay of entanglement…
A full strength Coulomb interaction between trapped electrons can be felt only in absence of a neutralizing background. In order to study quantum degenerate electrons without such a background, an external trap is needed to compensate for the strong electronic repulsion. As a basic model for such a system, we study a trapped electron pair in a harmonic trap with an explicit inclusion of its Coulomb interaction. We find the eigenenergy of the ground state, confirming earlier work in the context of harmonium. We extend this to a complete set of properly scaled energies for any value of the trapp…
We demonstrate electromagnetically induced transparency (EIT) in a sample of rubidium atoms, trapped in an optical dipole trap. Mixing a small amount of $σ^-$-polarized light to the weak $σ^+$-polarized probe pulses, we are able to measure the absorptive and dispersive properties of the atomic medium at the same time. Features as small as 4 kHz have been detected on an absorption line with 20 MHz line width.
We propose a generation method of Bell-type states involving light and the vibrational motion of a single trapped ion. The trap itself is supposed to be placed inside a high-$Q$ cavity sustaining a single mode, quantized electromagnetic field. Entangled light-motional states may be readily generated if a conditional measurement of the ion's internal electronic state is made after an appropriate interaction time and a suitable preparation of the initial state. We show that all four Bell states may be generated using different motional sidebands (either blue or red), as well as adequate ionic re…
We demonstrate a general method for state detection of trapped ions that can be applied to a large class of atomic and molecular species. We couple a "spectroscopy" ion (Al+) to a "control" ion (Mg+) in the same trap and perform state detection through off-resonant laser excitation of the spectroscopy ion that induces coherent motion. The motional amplitude, dependent on the spectroscopy ion state, is measured either by time-resolved photon counting, or by resolved sideband excitations on the control ion. The first method provides a simplified way to distinguish "clock" states in Al+, which av…
It is shown that general solutions of the free-particle Schroedinger equation can be mapped onto solutions of the Schroedinger equation for the harmonic oscillator. This is done in such a way that the time evolution of a free particle subjected to a sudden transition to a harmonic potential can be described by a simple coordinate transformation applied at the transition time. This procedure is computationally more efficient than either state-projection or propagator techniques. A concatenation of the map and its inverse allows us to map from one harmonic oscillator to another with a different …
A laser cooling scheme for trapped ions is presented which is based on the fast dynamical Stark shift gate, described in [Jonathan etal, PRA 62, 042307]. Since this cooling method does not contain an off resonant carrier transition, low final temperatures are achieved even in traveling wave light field. The proposed method may operate in either pulsed or continuous mode and is also suitable for ion traps using microwave addressing in strong magnetic field gradients.
Ordered atomic arrays trapped in the vicinity of nanoscale waveguides offer original light-matter interfaces, with applications to quantum information and quantum non-linear optics. Here, we study the decay dynamics of a single collective atomic excitation coupled to a waveguide in different configurations. The atoms are arranged as a linear array and only a segment of them is excited to a superradiant mode and emits light into the waveguide. Additional atomic chains placed on one or both sides play a passive role, either reflecting or absorbing this emission. We show that when varying the geo…
We propose a decoherence-free subspaces (DFS) scheme to realize scalable quantum computation with trapped ions. The spin-dependent Coulomb interaction is exploited, and the universal set of unconventional geometric quantum gates is achieved in encoded subspaces that are immune from decoherence by collective dephasing. The scalability of the scheme for the ion array system is demonstrated, either by an adiabatic way of switching on and off the interactions, or by a fast gate scheme with comprehensive DFS encoding and noise decoupling techniques.
We report continuous Raman sideband cooling (CRSC) of a long ion chain to the motional ground state beyond the Lamb-Dicke (LD) regime. By driving multiple sideband transitions simultaneously, we show that nearly all axial modes of a 24-ion chain are cooled to the ground state, with an LD parameter as large as $η= 1.3$, spanning a frequency bandwidth of 4 MHz. Compared to traditional ground-state cooling methods such as pulsed sideband cooling or electromagnetic-induced-transparency (EIT) cooling, our method offers two key advantages: robustness to timing errors; and an ultra-wide bandwidth unl…
The interaction of a trapped ion with a laser beam in the strong excitation regime is analyzed. In this regime, a variety of non--classical states of motion can be prepared either by using laser pulses of well defined area, or by an adiabatic passage scheme based on the variation of the laser frequency. We show how these states can be used to investigate fundamental properties of quantum mechanics. We also study possible applications of this system to build an ion interferometer.
The efficiency of cavity sideband cooling of trapped molecules is theoretically investigated for the case where the IR transition between two rovibrational states is used as a cycling transition. The molecules are assumed to be trapped either by a radio-frequency or optical trapping potential, depending on whether they are charged or neutral, and confined inside a high-finesse optical resonator which enhances radiative emission into the cavity mode. Using realistic experimental parameters and COS as a representative molecular example, we show that in this setup cooling to the trap ground state…
We developed a multi-mode ground state cooling technique based on electromagnetically-induced transparency (EIT). By involving an additional ground and excited state, two individually adjustable bright states together with a dark state are created. While the dark state suppresses carrier scattering, the two bright states are brought into resonance with spectrally separated motional red sidebands. With this double-bright EIT (D-EIT) cooling scheme, we experimentally demonstrate ground state cooling of all three motional modes of a trapped $^{40}$Ca$^+$ with a single cooling pulse. The approach …
Novel ion traps that provide either a static or a dynamic magnetic gradient field allow for the use of radio frequency (rf) radiation for coupling internal and motional states of ions, which is essential for conditional quantum logic. We show that the coupling mechanism in the presence of a dynamic gradient is the same, in a dressed state basis, as in the case of a static gradient. Then, it is shown how demanding experimental requirements arising when using a dynamic gradient could be overcome. Thus, using dressed states in a dynamic gradient field could decisively reduce experimental complexi…
We study the confinement of Dirac fermions in armchair graphene nanoribbons by means of a quantum-dot-type electrostatic potential. With the use of specific projection operators, we find exact solutions for some bound states that satisfy appropriate boundary conditions. We show that the energies of these bound states belong either to the gap of valence and conducting bands or they represent BIC's (bound states in the continuum) whose energies are embedded in the continuous spectrum.
We discuss a simple search problem which can be pursued with different methods, either on a classical or on a quantum basis. The system is represented by a chain of trapped ions. The ion to be searched is a member of that chain, consists, however, of an isotopic species different to the others. It is shown that the classical imaging may lead as fast to the final result as the quantum imaging. However, for the discussed case the quantum method gives more flexibility and higher precision when the number of ions considered in the chain is increasing. In addition, interferences are observable even…
We theoretically analyze the cooling dynamics of an atom which is tightly trapped inside a high-finesse optical resonator. Cooling is achieved by suitably tailored scattering processes, in which the atomic dipole transition either scatters a cavity photon into the electromagnetic field external to the resonator, or performs a stimulated emission into the cavity mode, which then dissipates via the cavity mirrors. We identify the parameter regimes in which the atom center-of-mass motion can be cooled into the ground state of the external trap. We predict, in particular, that for high cooperativi…
We propose a new dark-state cooling method of trapped ion systems in the Lamb-Dicke limit. With application of microwave dressing the ion, we can obtain two electromagnetically induced transparency structures. The heating effects caused by the carrier and the blue sideband transition vanish due to the EIT effects and the final mean phonon numbers can be much less than the recoil limit. Our scheme is robust to fluctuations of microwave power and laser intensities which provides a broad cooling bandwidth to cool motional modes of a linear ion chain. Moreover, it is more suitable to cool four-lev…
Quantum error-correcting codes are many-body entangled states that are prepared and measured using complex sequences of entangling operations. Each element of such an entangling sequence introduces noise to delicate quantum information during the encoding or reading out of the code. It is important therefore to find efficient entangling protocols to avoid the loss of information. Here we propose an experiment that uses only global entangling operations to encode an arbitrary logical qubit to either the five-qubit repetition code or the five-qubit code, with a six-ion Coulomb crystal architectu…
Trapped ions are among the most promising platforms for quantum technologies. They are at the heart of the most precise clocks and sensors developed to date, which exploit the quantum coherence of a single electronic or motional degree of freedom of an ion. However, future high precision quantum metrology will require the use of entangled states of several degrees of freedom. Here we propose a protocol capable of generating high N00N states where the entanglement is shared between the motion of a trapped ion and an electromagnetic cavity mode, a so called hybrid configuration. We prove the fea…
Cooling the trapped atoms toward their motional ground states is key to applications of quantum simulation and quantum computation. By utilizing nonreciprocal couplings between constituent atoms, we present an intriguing dark-state cooling scheme in $Λ$-type three-level structure, which is shown superior than the conventional electromagnetically-induced-transparency cooling in a single atom. The effective nonreciprocal couplings can be facilitated either by an atom-waveguide interface or a free-space photonic quantum link. By tailoring system parameters allowed in dark-state cooling, we identi…
We study the laser cooling of one atom in an harmonic trap beyond the Lamb-Dicke regime. By using sequences of laser pulses of different detunings we show that the atom can be confined into just one state of the trap, either the ground state or an excited state of the harmonic potential. The last can be achieved because under certain conditions an excited state becomes a dark state. We study the problem in one and two dimensions. For the latter case a new cooling mechanism is possible, based on the destructive interference between the effects of laser fields in different directions, which allo…
We demonstrate an optical method for detecting the mechanical oscillations of an atom with single-phonon sensitivity. The measurement signal results from the interference between the light scattered by a single trapped atomic ion and that of its mirror image. The motion of the atom modulates the interference path length and hence the photon detection rate. We detect the oscillations of the atom in the Doppler cooling limit and reconstruct average trajectories in phase space. We demonstrate single-phonon sensitivity near the ground state of motion after EIT cooling. These results could be appli…
We discuss continuous observation of the momentum of a single atom by employing the high velocity sensitivity of the index of refraction in a driven $Λ$-system based on electromagnetically induced transparency (EIT). In the ideal limit of unit collection efficiency this provides a quantum limited measurement with minimal backaction on the atomic motion. A feedback loop, which drives the atom with a force proportional to measured signal, provides a cooling mechanism for the atomic motion. We derive the master equation which describes the feedback cooling and show that in the Lamb-Dicke limit th…
We theoretically investigate the properties of a double-well bosonic Josephson junction coupled to a single trapped ion. We find that the coupling between the wells can be controlled by the internal state of the ion, which can be used for studying mesoscopic entanglement between the two systems and to measure their interaction with high precision. As a particular example we consider a single $^{87}$Rb atom and a small Bose-Einstein condensate controlled by a single $^{171}$Yb$^+$ ion. We calculate inter-well coupling rates reaching hundreds of Hz, while the state dependence amounts to tens of …
We systematically investigate the multi-stability behaviour and cooling of both librational and translational modes of an optically levitated nonspherical nanoparticle. By expanding the trapping potential to the fourth order of both the translational and librational freedom degrees, we deduce the nonlinearity of them and their nonlinear coupling. Through stability analysis, we find that the system presents multi-stability when either the librational or the translational drive is red-detuned. The system will be stabilized if and only if these two drives are both blue-detuned. In the steady stat…
We introduce and demonstrate double-bright electromagnetically induced transparency (D-EIT) cooling as a novel approach to EIT cooling. By involving an additional ground state, two bright states can be shifted individually into resonance for cooling of motional modes of frequencies that may be separated by more than the width of a single EIT cooling resonance. This allows three-dimensional ground state cooling of a $^{40}$Ca$^+$ ion trapped in a linear Paul trap with a single cooling pulse. Measured cooling rates and steady-state mean motional quantum numbers for this D-EIT cooling are compare…
Active quantum error correction has been identified as a crucial ingredient of future quantum computers, motivating the recent experimental efforts to encode logical quantum bits using small topological codes. In addition to the demonstration of the beneficial role of the encoding, a break-even point in the progress towards large-scale quantum computers will be the implementation of a universal set of gates. This mid-term challenge will soon be faced by various quantum technologies, which urges the need of realistic assessments of their prospects. In this work, we pursue this goal by assessing…
We study controlled phasegates for ultracold atoms in an optical potential. A shaped laser pulse drives transitions between the ground and electronically excited states where the atoms are subject to a long-range 1/R^3 interaction. We fully account for this interaction and use optimal control theory to calculate the pulse shapes. This allows us to determine the minimum pulse duration, respectively, gate time T that is required to obtain high fidelity. We accurately analyze the speed limiting factors, and we find the gate time to be limited either by the interaction strength in the excited stat…
We report experimental implementation of various types of qubit channels using an individual trapped ion. We analyzed experimental data and we performed tomographic reconstruction of quantum channels based on these data. Specifically, we studied phase damping channels, where the damping acts either in the xy-plane of the Bloch sphere or in an arbitrary plane that includes the origin of the Bloch sphere. We also experimentally realized and consequently analyzed quantum channels that in addition to phase damping affect also a polarization rotation. We used three reconstruction schemes for estima…
We theoretically analyze the dynamics of an atomic double-well system with a single ion trapped in its center. We find that the atomic tunnelling rate between the wells depends both on the spin of the ion via the short-range spin-dependent atom-ion scattering length and on its motional state with tunnelling rates reaching hundreds of Hz. A protocol is presented that could transport an atom from one well to the other depending on the motional (Fock) state of the ion within a few ms. This phonon-atom coupling is of interest for creating atom-ion entangled states and may form a building block in …
Electromagnetically induced transparency (EIT) cooling has established itself as one of the most widely used cooling schemes for trapped ions during the past twenty years. Compared to its alternatives, EIT cooling possesses important advantages such as a tunable effective linewidth, a very low steady state phonon occupation, and applicability for multiple ions. However, existing analytic expression for the steady state phonon occupation of EIT cooling is limited to the zeroth order of the Lamb-Dicke parameter. Here we extend such calculations and present the explicit expression to the second o…
A quantum information processor is proposed that combines experimental techniques and technology successfully demonstrated either in nuclear magnetic resonance experiments or with trapped ions. An additional inhomogenenous magnetic field applied to an ion trap i) shifts individual ionic resonances (qubits), making them distinguishable by frequency, and, ii) mediates the coupling between internal and external degrees of freedom of trapped ions. This scheme permits one to individually address and coherently manipulate ions confined in an electrodynamic trap using radiation in the radiofrequency …
