We present the constructon and detailed analysis of highly-optimized self-refocusing pulse shapes for several rotation angles. We characterize the constructed pulses by the coefficients appearing in the Magnus expansion up to second order. This allows a semi-analytical analysis of the performance of the constructed shapes in sequences and composite pulses by computing the corresponding leading-order error operators. Higher orders can be analyzed with the numerical technique suggested by us previously. We illustrate the technique by analysing several composite pulses designed to protect against pulse amplitude errors, and on decoupling sequences for potentially long chains of qubits with on-site and nearest-neighbor couplings.
The realisation of optically detected magnetic resonance via nitrogen vacancy centers in diamond faces challenges at high magnetic fields which include growing energy consumption of control pulses as well as decreasing sensitivities. Here we address these challenges with the design of shaped pulses in microwave control sequences that achieve orders magnitude reductions in energy consumption and concomitant increases in sensitivity when compared to standard top-hat microwave pulses. The method proposed here is general and can be applied to any quantum sensor subjected to pulsed control sequence…
We developed single-shot shaped pulses for ultra high fidelity (UH-fidelity) population transfer on a 3-level quantum system in lambda configuration. To ensure high fidelity, we use the Lewis-Riesenfeld (L-R) method to derive a family of solutions leading to an exact transfer, where the solutions follow a single dynamical mode of the L-R invariant. Among this family, we identify a tracking solution with a single parameter to control simultaneously the fidelity of the transfer, the population of the excited state, and robustness. We define a measure of the robustness of an UH-fidelity transfer …
High fidelity quantum control over qubits is of crucial importance for realistic quantum computing, and it turns to be more challenging when there are inevitable interactions among qubits. By employing a bandselective shaped pulse, we demonstrate a high fidelity flip over electron spin of nitrogen-vacancy (NV) centers in diamond. In contrast with traditional rectangular pulses, the shaped pulse has almost equal excitation effect among a sharply edged region (in frequency domain). So the three sub-levels of host $^{14}N$ nuclear spin can be flipped accurately at the same time, while the redunda…
We propose a method to deterministically prepare a desired quantum state in a one-dimensional (1D) continuum by a shaped photon pulse. This method is based on time-reverse of the quantum emission process. We show that the desired quantum state such as Dicke or timed-Dicke state can be successfully prepared with very high fidelity even if the dissipation to the environment is nonnegligible and the pulse shaping is not perfect. We also show that large quantum entanglement between emitters can be created by just a single photon pulse. This method is experimentally feasible in 1D waveguide-QED or …
We employ Optimal Control Theory to discover an efficient information retrieval algorithm that can be performed on a Rydberg atom data register using a shaped terahertz pulse. The register is a Rydberg wave packet with one consituent orbital phase-reversed from the others (the ``marked bit''). The terahertz pulse that performs the decoding algorithm does so by by driving electron probability density into the marked orbital. Its shape is calculated by modifying the target of an optimal control problem so that it represents the direct product of all correct solutions to the algorithm.
Spontaneous Raman emission in atomic gases provides an attractive source of photon pairs with a controllable delay. We show how this technique can be implemented in solid state systems by appropriately shaping the inhomogeneous broadening. Our proposal is eminently feasible with current technology and provides a realistic solution to entangle remote rare-earth doped solids in a heralded way.
We present a general and versatile technique of population transfer based on {\it parallel adiabatic passage} by femtosecond shaped pulses. Their amplitude and phase are specifically designed to optimize the adiabatic passage corresponding to parallel eigenvalues at all times. We show that this technique allows the robust adiabatic population transfer in a Raman system with the total pulse area as low as 3 $π$, corresponding to a fluence of one order of magnitude below the conventional stimulated Raman adiabatic passage process. This process of short duration, typically pico- and subpicosecond…
We investigate the application of amplitude-shaped control pulses for enhancing the time and frequency resolution of multipulse quantum sensing sequences. Using the electronic spin of a single nitrogen vacancy center in diamond and up to 10,000 coherent microwave pulses with a cosine square envelope, we demonstrate 0.6 ps timing resolution for the interpulse delay. This represents a refinement by over 3 orders of magnitude compared to the 2 ns hardware sampling. We apply the method for the detection of external AC magnetic fields and nuclear magnetic resonance signals of carbon-13 spins with h…
Considering the problem of the control of a two-state quantum system by an external field, we establish a general and versatile method that allows the derivation of smooth pulses, suitable for ultrafast applications, that feature the properties of high-fidelity, robustness, and low area. Such shaped pulses can be viewed as a single-shot generalization of the composite pulse technique with a time-dependent phase.
We report and propose a simple scheme to achieve efficient and fast coherent population transfer (CPT) by utilizing either a nonlinearly chirped Gaussian shaped few-cycle laser pulse or an unchirped sinc-shaped few-cycle laser pulse. The proposed scheme is shown to be fairly robust against the variation of the laser parameters such as temporal pulse width, chirp rates, carrier envelope phases and Rabi frequencies. We find that compared to the so-called stimulated Raman adiabatic passage (STIRAP) technique, our scheme for complete population transfer with few-cycle Gaussian shaped laser pulses …
We show that the use of shaped pulses improves the fidelity of a Rydberg blockade two-qubit entangling gate by several orders of magnitude compared to previous protocols based on square pulses or optimal control pulses. Using analytical Derivative Removal by Adiabatic Gate (DRAG) pulses that reduce excitation of primary leakage states and an analytical method of finding the optimal Rydberg blockade we generate Bell states with a fidelity of $F>0.9999$ in a 300 K environment for a gate time of only $50\;{\rm ns}$, which is an order of magnitude faster than previous protocols. These results esta…
In this paper we study robust pulse design for electron shuttling in solid state devices. This is crucial for many practical applications of coherent quantum mechanical systems. Our objective is to design control pulses that can transport an electron along a chain of donors, and also make this process robust to parameter uncertainties. We formulate it as a set of optimal control problems on the special unitary group SU(n), and derive explicit expressions for the gradients of the aggregate transfer fidelity. Numerical results for a donor chain of ionized phosphorus atoms in bulk silicon demonst…
Free electrons provide a powerful tool to probe material properties at atomic-scale spatial resolution. Recent advances in ultrafast electron microscopy enable the manipulation of free electron wavefunctions using laser pulses. It would be of great importance if one could combine the spatial resolution of electron probes with the ability of laser pulses to probe coherent phenomena in quantum systems. To this end, we propose a novel technique that leverages free electrons that are coherently-shaped by laser pulses to measure quantum coherence in materials. Developing a quantum theory of electro…
The explicit criterion is derived in detail for the convergence of the Magnus expansion and the existence of the Magnus solution in the interaction picture, i.e., the exponential propagator in the weakly coupled spin (I=1/2) system SnAMX... (n=1,2,3,...) in which only spin group S is subjected to a time-dependent shaped selective radiofrequency pulse. The derivation is built on the same scheme as the Maricq's (J. Chem. Phys. 86 (1987) 5647). It is shown that the criterion depends only upon amplitude of the time-dependent field applied to the system, and the Magnus expansion converges and the M…
Quantum computation requires high-fidelity single-qubit and two-qubit gates on a scalable platform. Silicon spin qubits are a promising platform toward realization of this goal. In this paper we show how to perform single-qubit and CZ gates in a linear chain of three spin qubits with always-on exchange coupling, which is relevant for certain dot- and donor-based silicon devices. We also show how to make the CZ gate robust against both charge noise and pulse length error using a two-tone pulse shaping method. The robust pulse maintains a fidelity of 99.99% at 3.5% fluctuations in exchange or pu…
Laser cooling of molecules employing broadband optical pumping involves a timescale separation between laser excitation and spontaneous emission. Here, we optimize the optical pumping step using shaped laser pulses. We derive two optimization functionals to drive population into those excited state levels that have the largest spontaneous emission rates to the target state. We show that, when using optimal control, laser cooling of molecules works even if the Franck-Condon map governing the transitions is preferential to heating rather than cooling. Our optimization functional is also applicab…
Electronic spin-qubit is key ingredient for quantum information processing in a solid state environment. We present a $π$-shaped two-qubit entanglement device capable of measuring the resultant states in Bell basis. In our device, source spins ($\uparrow_s$ or $\downarrow_s$) are electrically generated and tunnelled to channel where they interact with channel spins ($\uparrow_c$ or $\downarrow_c$) via exchange interaction which is responsible for 2-qubit entanglement. Electrical control over spins gives rise to the Bell states. The $U_{\sqrt{SWAP}}$ and CNOT gate operations are implemented thr…
We have constructed an automated learning apparatus to control quantum systems. By directing intense shaped ultrafast laser pulses into a variety of samples and using a measurement of the system as a feedback signal, we are able to reshape the laser pulses to direct the system into a desired state. The feedback signal is the input to an adaptive learning algorithm. This algorithm programs a computer-controlled, acousto-optic modulator pulse shaper. The learning algorithm generates new shaped laser pulses based on the success of previous pulses in achieving a predetermined goal.
The ability to entangle distant quantum nodes is essential for the construction of quantum networks and for quantum information processing. For solid-state quantum emitters used as qubits, it can be achieved by photon interference. When the emitter is subject to spectral diffusion, this process can become highly inefficient, impeding the achievement of scalable quantum technologies. We study two-photon interference in the context of a Hong-Ou-Mandel (HOM)-type experiment for two separate quantum emitters, with different detunings with respect to a specific target frequency. We evaluate the sec…
We demonstrate the control of the alpha-proton nuclear spin, I=1/2, coupled to the stable radical CH(COOH)2, S=1/2, in a gamma-irradiated malonic acid single crystal using only microwave pulses. We show that, depending on the state of the electron spin mS=+/-1/2, the nuclear spin can be locked in a desired state or oscillate between mI=+1/2 and mI=-1/2 on the nanosecond time scale. This approach provides a fast and efficient way of controlling nuclear spin qubits and also enables the design of switchable spin-based quantum gates by addressing only the electron spin.
Two-photon excitation (TPE) proceeds via a "virtual" pathway, which depends on the accessibility of one or more intermediate states, and, in the case of non-centrosymmetric molecules, an additional "dipole" pathway involving the off-resonance dipole-allowed one-photon transitions and the change in the permanent dipole moment between the initial and final states. Here, we control the quantum interference between these two optical excitation pathways by using phase-shaped femtosecond laser pulses. We find enhancements by a factor of up to 1.75 in the two-photon-excited fluorescence of the photob…
We report on the application of a dynamic decoherence control pulse sequence on a nuclear quadrupole transition in $Pr^{3+}:Y_2SiO_5$ . Process tomography is used to analyse the effect of the pulse sequence. The pulse sequence was found to increase the decoherence time of the transition to over 30 seconds. Although the decoherence time was significantly increased, the population terms were found to rapidly decay on the application of the pulse sequence. The increase of this decay rate is attributed to inhomogeneity in the ensemble. Methods to circumvent this limit are discussed.
The first step in the coherent control of a photoinduced binary reaction is bond making or photoassociation. We have recently demonstrated coherent control of bond making in multi-photon femtosecond photoassociation of hot magnesium atoms, using linearly chirped pulses [Levin et al., arXiv:1411.1542]. The detected yield of photoassociated magnesium dimers was enhanced by positively chirped pulses which is explained theoretically by a combination of purification and chirp-dependent Raman transitions. The yield could be further enhanced by pulse optimization resulting in pulses with an effective…
Non Born-Oppenheimer quantum dynamics of H$_{2}^{+}$ excited by shaped one-cycle laser pulses linearly polarized along the molecular axis have been studied by the numerical solution of the time-dependent Schrödinger equation within a %three-body three-dimensional model, including the internuclear separation, $R$, and the electron coordinates $z$ and $ρ$. Laser carrier frequencies corresponding to the wavelengths $λ_{l}=25$~nm through $λ_{l}=400$~nm were used and the amplitudes of the pulses were chosen such that the energy of H$_{2}^{+}$ was close to its dissociation threshold at the end of an…
The efficiency of dipole-dipole coupling driven coherence transfer experiments in solid-state NMR spectroscopy of powder samples is limited by dispersion of the orientation of the internuclear vectors relative to the external magnetic field. Here we introduce general design principles and resulting pulse sequences that approach full polarization transfer efficiency for all crystallite orientations in a powder in magic-angle-spinning experiments. The methods compensate for the defocusing of coherence due to orientation dependent dipolar coupling interactions and inhomogeneous radio-frequency fi…
We describe how the spin coherence time of a localized electron spin in solids, i.e. a solid state spin qubit, can be prolonged by applying designed electron spin resonance pulse sequences. In particular, the spin echo decay due to the spectral diffusion of the electron spin resonance frequency induced by the non-Markovian temporal fluctuations of the nuclear spin flip-flop dynamics can be strongly suppressed using multiple-pulse sequences akin to the Carr-Purcell-Meiboom-Gill pulse sequence in nuclear magnetic resonance. Spin coherence time can be enhanced by factors of 4-10 in GaAs quantum d…
Optimal control experiments can readily identify effective shaped laser pulses, or "photonic reagents", that achieve a wide variety of objectives. For many practical applications, an important criterion is that a particular photonic reagent prescription still produce a good, if not optimal, target objective yield when transferred to a different system or laboratory, {even if the same shaped pulse profile cannot be reproduced exactly. As a specific example, we assess the potential for transferring optimal photonic reagents for the objective of optimizing a ratio of photoproduct ions from a fami…
NMR spin echo measurements of C-13 in C60, Y-89 in Y2O3, and Si-29 in silicon are shown to defy conventional expectations when more that one pi pulse is used. Multiple pi-pulse echo trains may either freeze our or accelerate the decay of the signal, depending on the pi-pulse phase. Average Hamiltonian theory, combined with exact quantum calculations, reveals an intrinsic cause for these coherent phenomena: the dipolar coupling has a many-body effect during any real, finite pulse.
The processes of ionization and energy transfer in a quantum system composed of two distant H atoms with an initial internuclear separation of 100 atomic units (5.29 nm) have been studied by the numerical solution of the time-dependent Schrödinger equation beyond the Born-Oppenheimer approximation. Thereby it has been assumed that only one of the two H atoms was excited by temporally and spatially shaped laser pulses at various laser carrier frequencies. The quantum dynamics of the extended H-H system, which was taken to be initially either in an unentangled or an entangled ground state, has b…
We present a framework that uses a continuous frequency space to describe and design solid-state NMR experiments. The approach is similar to the well established Floquet treatment for NMR, but is not restricted to periodic Hamiltonians and allows the design of experiments in a reverse fashion. The framework is based on perturbation theory on a continuous Fourier space, which leads to effective, i.e., time-independent, Hamiltonians. It allows the back calculation of the pulse scheme from the desired effective Hamiltonian as a function of spin-system parameters. We show as an example how to back…
In spectroscopy, it is conventional to treat pulses much stronger than the linewidth as delta-functions. In NMR, this assumption leads to the prediction that pi pulses do not refocus the dipolar coupling. However, NMR spin echo measurements in dipolar solids defy these conventional expectations when more than one pi pulse is used. Observed effects include a long tail in the CPMG echo train for short delays between pi pulses, an even-odd asymmetry in the echo amplitudes for long delays, an unusual fingerprint pattern for intermediate delays, and a strong sensitivity to pi-pulse phase. Experimen…
The application of Carr-Purcell-Meiboom-Gill (CPMG) $π-$trains for dynamically decoupling a system from its environment has been extensively studied in a variety of physical systems. When applied to dipolar solids, recent experiments have demonstrated that CPMG pulse trains can generate long-lived spin echoes. While there still remains some controversy as to the origins of these long-lived spin echoes under the CPMG sequence, there is a general agreement that pulse errors during the $π-$pulses are a necessary requirement. In this work, we develop a theory to describe the spin dynamics in dipol…
Coherent control over photoelectron wavepackets, via the use of polarization-shaped laser pulses, can be understood as a time and polarization-multiplexed process. In this work, we investigate this multiplexing via computation of the observable photoelectron angular interferograms resulting from multi-photon atomic ionization with polarization-shaped laser pulses. We consider the polarization sensitivity of both the instantaneous and cumulative continuum wavefunction; the nature of the coherent control over the resultant photoelectron interferogram is thus explored in detail. Based on this und…
The sensitivity of quantum magnetometers is challenged by control errors and, especially in the solid-state, by their short coherence times. Refocusing techniques can overcome these limitations and improve the sensitivity to periodic fields, but they come at the cost of reduced bandwidth and cannot be applied to sense static (DC) or aperiodic fields. Here we experimentally demonstrate that continuous driving of the sensor spin by a composite pulse known as rotary-echo (RE) yields a flexible magnetometry scheme, mitigating both driving power imperfections and decoherence. A suitable choice of R…
Metal atoms in solid and liquid helium-4 have attracted some interest either as a way to keep the atoms in a weakly perturbing matrix, or using them as a probe for the helium host medium. Laser sputtering with nanosecond pulsed lasers is the most often used method for atom production, resulting however in a substantial perturbation of the matrix. We show that a much weaker perturbation can be obtained by using femtosecond laser pulses with energy as low as 10 $μ$J. As an unexpected benefit, the atomic density produced is much higher.
Quantum repeaters are critical components for distributing entanglement over long distances in presence of unavoidable optical losses during transmission. Stimulated by Duan-Lukin-Cirac-Zoller protocol, many improved quantum-repeater protocols based on quantum memories have been proposed, which commonly focus on the entanglement-distribution rate. Among these protocols, the elimination of multi-photons (multi-photon-pairs) and the use of multimode quantum memory are demonstrated to have the ability to greatly improve the entanglement-distribution rate. Here, we demonstrate the storage of deter…
Transitions in an artificial atom, driven non-adiabatically through an energy-level avoided crossing, can be controlled by carefully engineering the driving protocol. We have driven a superconducting persistent-current qubit with a large-amplitude, radio-frequency field. By applying a bi-harmonic waveform generated by a digital source, we demonstrate a mapping between the amplitude and phase of the harmonics produced at the source and those received by the device. This allows us to image the actual waveform at the device. This information is used to engineer a desired time dependence, as confi…
We predict a strong-field ultrafast optical Faraday effect, where a circularly polarized ultrashort optical pulse induces transient chirality in an achiral transparent dielectric. This effect is attractive for time-resolved measurements because it gives access to the non-instantaneity of the nonlinear medium response, and also because it represents relaxation of time-reversal symmetry by all-optical means. We propose probing the induced transient chirality with a weak linearly polarized ultraviolet pulse that is shorter than the near-infrared pump pulse. The predicted effects are ultrafast: th…
In many quantum architectures the solid-state qubits, such as quantum dots or color centers, are interfaced via emitted photons. However, the frequency of photons emitted by solid-state systems exhibits slow uncontrollable fluctuations over time (spectral diffusion), creating a serious problem for implementation of the photon-mediated protocols. Here we show that a sequence of optical pulses applied to the solid-state emitter can stabilize the emission line at the desired frequency. We demonstrate efficiency, robustness, and feasibility of the method analytically and numerically. Taking nitrog…
