arXiv subjects

Nikolay V. Vitanov

Publications and source records attributed to Nikolay V. Vitanov.

At least 55 records · Page 3Linked to original sources

arXiv2020

High-fidelity composite quantum gates for Raman qubits

We present a general systematic approach to design robust and high-fidelity quantum logic gates with Raman qubits using the technique of composite pulses. We use two mathematical tools -- the Morris-Shore and Majorana decompositions -- to reduce the three-state Raman system to an equivalent two-state system. They allow us to exploit the numerous composite pulses designed for two-state systems by extending them to Raman qubits. We construct the NOT, Hadamard, and rotation gates by means of the Morris-Shore transformation with the same uniform approach: sequences of pulses with the same phases for each gate but different ratios of Raman couplings. The phase gate is constructed by using the Majorana decomposition. All composite Raman gates feature very high fidelity, beyond the quantum computation benchmark values, and significant robustness to experimental errors. All composite phases and pulse areas are given by analytical formulas, which makes the method scalable to any desired accuracy and robustness to errors.

quant-ph↗

arXiv2020

Narrowband and passband composite pulses for variable rotations

We develop a systematic approach to derive narrowband (NB) and passband (PB) composite sequences which can produce any pre-selected transition probability with any desired accuracy. The NB composite pulses are derived by successive cancellation of derivative terms in the propagator. The PB pulses are built by combining two half-$π$ NB pulses. Both the NB and PB pulses feature vanishing wings on both sides of the central region around the target transition probability, and the PB pulses offer also a flat (broadband) top around the target probability. The NB sequences are particularly suitable for sensing and metrology applications, while the PB sequences can be very useful for qubit control in the case of tightly spaced qubits for they ensure both selectivity (suppressed cross talk to neighbors) and robustness (suppressed laser pointing instability). Other possible applications include selective (NB), or both selective and robust (PB), control of close transitions in frequency space.

quant-ph↗

arXiv2020

High-fidelity multistate STIRAP assisted by shortcut fields

Multistate stimulated Raman adiabatic passage (STIRAP) is a process which allows for adiabatic population transfer between the two ends of a chainwise-connected quantum system. The process requires large temporal areas of the driving pulsed fields (pump and Stokes) in order to suppress the nonadiabatic couplings and thereby to make adiabatic evolution possible. To this end, in the present paper a variation of multistate STIRAP, which accelerates and improves the population transfer, is presented. In addition to the usual pump and Stokes fields it uses shortcut fields applied between the states, which form the dark state of the system. The shortcuts cancel the couplings between the dark state and the other adiabatic states thereby resulting (in the ideal case) in a unit transition probability between the two end states of the chain. Specific examples of five-state systems formed of the magnetic sublevels of the transitions between two degenerate levels with angular momenta $J_g=2$ and $J_e=1$ or $J_e=2$ are considered in detail, for which the shortcut fields are derived analytically. The proposed method is simpler than the usual "shortcuts to adiabaticity" recipe, which prescribes shortcut fields between all states of the system, while the present proposal uses shortcut fields between the sublevels forming the dark state only. The results are of potential interest in applications where high-fidelity quantum control is essential, e.g. quantum information, atom optics, formation of ultracold molecules, cavity QED, etc.

quant-ph↗

arXiv2020

Universal Composite Pulses for Efficient Population Inversion with an Arbitrary Excitation Profile

We introduce a method to rotate arbitrarily the excitation profile of universal broadband composite pulse sequences for robust high-fidelity population inversion. These pulses compensate deviations in any experimental parameter (e.g. pulse amplitude, pulse duration, detuning from resonance, Stark shifts, unwanted frequency chirp, etc.) and are applicable with any pulse shape. The rotation allows to achieve higher order robustness to any combination of pulse area and detuning errors at no additional cost. The latter can be particularly useful, e.g., when detuning errors are due to Stark shifts that are correlated with the power of the applied field. We demonstrate the efficiency and universality of these composite pulses by experimental implementation for rephasing of atomic coherences in a $\text{Pr}^{3+}\text{:}\text{Y}_2\text{SiO}_5\:$ crystal.

quant-ph↗

arXiv2020

Efficient and robust chiral resolution by composite pulses

We introduce a method for detection of chiral molecules using sequences of three pulses driving a closed-loop three-state quantum system. The left- and right-handed enantiomers have identical optical properties (transition frequencies and transition dipole moments) with the only difference being the sign of one of the couplings. We identify twelve different sequences of resonant pulses for which chiral resolution with perfect contrast occurs. In all of them the first and third pulses are $π/2$-pulses and the middle pulse is a $π$-pulse. In addition, one of the three pulses must have a phase shift of $π/2$ with respect to the other two. The simplicity of the proposed chiral resolution technique allows for straightforward extensions to more efficient and more robust implementations by replacing the single $π/2$ and $π$-pulses by composite pulses. We present specific examples of chiral resolution by composite pulses which compensate errors in the pulse areas and the detuning of the driving fields.

quant-ph↗

arXiv2020

Two-qubit quantum Fourier transform and entanglement protected by circulant symmetry

We propose a method for the realization of the two-qubit quantum Fourier transform (QFT) using a Hamiltonian which possesses the circulant symmetry. Importantly, the eigenvectors of the circulant matrices are the Fourier modes and do not depend on the magnitude of the Hamiltonian elements as long as the circulant symmetry is preserved. The QFT implementation relies on the adiabatic transition from each of the spin product states to the respective quantum Fourier superposition states. We show that in ion traps one can obtain a Hamiltonian with the circulant symmetry by tuning the spin-spin interaction between the trapped ions. We present numerical results which demonstrate that very high fidelity can be obtained with realistic experimental resources. We also describe how the gate can be accelerated by using a "shortcut-to-adiabaticity" field.

quant-ph↗

arXiv2019

Master equation approach to the three-state open Majorana model

The three-state Majorana model in the presence of dissipation is considered. Different models of system-environment interaction are explored, ranging from situation where dissipation is the main effect to regimes where dephasing is mainly produced. It is shown that the detrimental effects of the noise are stronger in the presence of dissipation than in the presence of dephasing. The role of temperature is also discussed.

quant-ph↗

arXiv2019

Achromatic polarization rotator with tunable rotation angle

We theoretically suggest and experimentally demonstrate a broadband composite optical rotator that is capable of rotating the polarization plane of a linearly-polarized light at any chosen angle. The device is composed of an even number of half-wave plates rotated at specific angles with respect to their fast-polarization axes. The frequency bandwidth of the polarization rotator in principal increases with the number of half-wave plates. Here we experimentally examine the performance of rotators composed of two, four, six, eight and ten half-wave plates.

physics.optics↗

arXiv2019

Generation of arbitrary qubit states by adiabatic evolution split by a phase jump

We propose a technique for accurate, flexible and robust generation of arbitrary coherent superpositions of two quantum states. It uses a sequence of two adiabatic pulses split by a phase jump serving as a control parameter. Each pulse has a chirped detuning, which induces a half crossing, and acts as a $π/2$ pulse in the adiabatic regime. The phase jump is imprinted onto the population ratio of the created superposition state. Of the various possible relations between the two pulses, we select the case when the Rabi frequency and the detuning of the second pulse are mirror images of those of the first pulse, and the two detunings have opposite signs. Then the mixing angle of the superposition state depends on the phase jump only. For other arrangements, the superposition mixing angle is shifted by the dynamic phases of the propagators, which makes these cases suitable for state tomography. This twin setup comes along with the advantage that it reduces the error $ε$ of each individual pulse down to $4ε^2$ overall. Therefore, the proposed technique combines the benefits of robustness stemming from adiabatic evolution with accuracy generated by the twin-pulse error suppression, and flexibility of the superposition state controlled by the phase jump $ϕ$. In addition, we present a simple exactly soluble trigonometric model in order to illustrate the proposed technique. In this model, when the pulse area $A$ increases the nonadiabatic oscillations are damped as $A^{-1}$ for a single pulse and $A^{-2}$ for the two-pulse sequence. Finally, the proposed technique is extended to sequences of $N=2^n$ pulses by concatenating $π/2$ sequences and splitting them by a phase jump, thereby further reducing the nonadiabatic error $ε$ to $(2ε)^{N}$. This makes the proposed technique suitable for generating high-fidelity quantum rotation gates.

quant-ph↗

arXiv2019

Roadmap on STIRAP applications

STIRAP (Stimulated Raman Adiabatic Passage) is a powerful laser-based method, usually involving two photons, for efficient and selective transfer of population between quantum states. A particularly interesting feature is the fact that the coupling between the initial and the final quantum states is via an intermediate state even though the lifetime of the latter can be much shorter than the interaction time with the laser radiation. Nevertheless, spontaneous emission from the intermediate state is prevented by quantum interference. Maintaining the coherence between the initial and final state throughout the transfer process is crucial. STIRAP was initially developed with applications in chemical dynamics in mind. That is why the original paper of 1990 was published in The Journal of Chemical Physics. However, as of about the year 2000, the unique capabilities of STIRAP and its robustness with respect to small variations of some experimental parameters stimulated many researchers to apply the scheme in a variety of other fields of physics. The successes of these efforts are documented in this collection of articles.

quant-ph↗

arXiv2019

Relations between the single-pass and multi-pass qubit gate errors

In quantum computation the target fidelity of the qubit gates is very high, with the admissible error being in the range from $10^{-3}$ to $10^{-4}$ and even less, depending on the protocol. The direct experimental determination of such an extremely small error is very challenging by standard quantum-process tomography. Instead, the method of randomized benchmarking, which uses a random sequence of Clifford gates, has become a standard tool for determination of the average gate error as the decay constant in the exponentially decaying fidelity. In this paper, the task for determining a tiny error is addressed by sequentially repeating the \emph{same} gate multiple times, which leads to the coherent amplification of the error, until it reaches large enough values to be measured reliably. If the transition probability is $p=1-ε$ with $ε\ll 1$ in the single process, then classical intuition dictates that the probability after $N$ passes should be $P_N \approx 1 - N ε$. However, this classical expectation is misleading because it neglects interference effects. This paper presents a rigorous theoretical analysis based on the SU(2) symmetry of the qubit propagator, resulting in explicit analytic relations that link the $N$-pass propagator to the single-pass one in terms of Chebyshev polynomials. In particular, the relations suggest that in some special cases the $N$-pass transition probability degrades as $P_N = 1-N^2ε$, i.e. dramatically faster than the classical probability estimate. In the general case, however, the relation between the single-pass and $N$-pass propagators is much more involved. Recipes are proposed for unambiguous determination of the gate errors in the general case, and for both Clifford and non-Clifford gates.

quant-ph↗

arXiv2019

Composite pulses with errant phases

Composite pulses --- sequences of pulses with well defined relative phases --- are an efficient, robust and flexible technique for coherent control of quantum systems. Composite sequences can compensate a variety of experimental errors in the driving field (e.g. in the pulse amplitude, duration, detuning, chirp, etc.) or in the quantum system and its environment (e.g. inhomogeneous broadening, stray electric or magnetic fields, unwanted couplings, etc.). The control parameters are the relative phases between the constituent pulses in the composite sequence, an accurate control over which is required in all composite sequences reported hitherto. In this paper, we introduce two types of composite pulse sequences which, in addition to error compensation in the basic experimental parameters, compensate systematic errors in the composite phases. In the first type of such composite sequences, which compensate pulse area errors, relative phase errors of up to 10% can be tolerated with reasonably short sequences while maintaining the fidelity above the 99.99% quantum computing benchmark. In the second type of composite sequences, which compensate pulse area and detuning errors, relative phase errors of up to 5% can be compensated.

quant-ph↗

arXiv2019

Compensation of the trap-induced quadrupole interaction in trapped Rydberg ions

The quadrupole interaction between the Rydberg electronic states of a Rydberg ion and the radio frequency electric field of the ion trap is analyzed. Such a coupling is negligible for the lowest energy levels of a trapped ion but it is important for a trapped Rydberg ion due to its large electric dipole moment. This coupling cannot be neglected by the standard rotating-wave approximation because it is comparable to the frequency of the trapping electric field. We investigate the effect of the quadrupole coupling by performing a suitable effective representation of the Hamiltonian. For a single ion we show that in this effective picture the quadrupole interaction is replaced by rescaled laser intensities and additional Stark shifts of the Rydberg levels. Hence this detrimental quadrupole coupling can be efficiently compensated by an appropriate increase of the Rabi frequencies. Moreover, we consider the strong dipole-dipole interaction between a pair of Rydberg ions in the presence of the quadrupole coupling. In the effective representation we observe reducing of the dipole-dipole coupling as well as additional spin-spin interaction.

quant-ph↗

arXiv2019

Optically-Induced Highly-Efficient Detection and Separation of Chiral Molecules through Shortcuts to Adiabaticity

A highly-efficient method for optical detection and separation of left- and right-handed chiral molecules is presented. The method utilizes a closed-loop three-state system in which the population dynamics depends on the phases of the three couplings. Due to the different signs of the coupling between two of the states for the opposite chiralities and the phase sensitivity of the scheme, the population dynamics is chirality-dependent. By using concepts from the `shortcuts to adiabaticity' approach, one can achieve 100\% contrast in state population transfer between the two enantiomers, which can be probed by light-induced fluorescence in the case of large ensembles or through resonantly-enhanced multiphoton ionization at the single molecular level.

quant-ph↗

arXiv2018

Experimental demonstration of composite stimulated Raman adiabatic passage

We experimentally demonstrate composite stimulated Raman adiabatic passage (CSTIRAP), which combines the concepts of composite pulse sequences and adiabatic passage. The technique is applied for population transfer in a rare-earth doped solid. We compare the performance of CSTIRAP with conventional single and repeated STIRAP, either in the resonant or the highly detuned regime. In the latter case, CSTIRAP improves the peak transfer efficiency and robustness, boosting the transfer efficiency substantially compared to repeated STIRAP. We also propose and demonstrate a universal version of CSTIRAP, which shows improved performance compared to the originally proposed composite version. Our findings pave the way towards new STIRAP applications, which require repeated excitation cycles, e.g., for momentum transfer in atom optics, or dynamical decoupling to invert arbitrary superposition states in quantum memories.

quant-ph↗

arXiv2018

Arbitrarily accurate variable rotations on the Bloch sphere by composite pulse sequences

Composite pulse sequences, which produce arbitrary pre-defined rotations of a two-state system at an angle $θ$ on the Bloch sphere, are presented. The composite sequences can contain arbitrarily many pulses and can compensate experimental errors in the pulse amplitude and duration to any desired order. A special attention is devoted to two classes of $π/2$ sequences --- symmetric and asymmetric --- the phases of which are given by simple formulas in terms of rational multiples of $π$ for any number of constituent pulses. This allows one to construct arbitrarily accurate $π/2$ composite rotations. These $π/2$ composite sequences are used to construct three classes of arbitrarily long composite $θ$ sequences by pairing two $π/2$ composite sequences, one of which is shifted by a phase $π-θ$ with respect to the other one.

quant-ph↗

arXiv2018

Robust high-fidelity coherent control of two-state systems by detuning pulses

Coherent control of two-state systems is traditionally achieved by resonant pulses of specific Rabi frequency and duration, by adiabatic techniques using level crossings or delayed pulses, or by sequences of pulses with precise relative phases (composite pulses). Here we develop a method for high-fidelity coherent control which uses a sequence of detuning pulses. By using the detuning pulse areas as control parameters, and driving on an analogy with composite pulses, we report a great variety of detuning pulse sequences for broadband and narrowband transition probability profiles.

quant-ph↗

arXiv2018

Arbitrarily accurate twin composite $π$ pulse sequences

We present three classes of symmetric broadband composite pulse sequences. The composite phases are given by analytic formulas (rational fractions of $π$) valid for any number of constituent pulses. The transition probability is expressed by simple analytic formulas and the order of pulse area error compensation grows linearly with the number of pulses. Therefore, any desired compensation order can be produced by an appropriate composite sequence; in this sense, they are arbitrarily accurate. These composite pulses perform equally well or better than previously published ones. Moreover, the current sequences are more flexible as they allow total pulse areas of arbitrary integer multiples of $π$.

quant-ph↗