Off-resonant Transitions Research Articles

Optimizing population accumulation in a designated single Zeeman state using microwave spectroscopy

We present an all-optical method for the highly efficient preparation of cold atoms in a specific Zeeman state, such as the magnetically insensitive clock state (m F = 0) or a particular state suitable for quantum information processing and storage. This technique employs a single microwave spectrum, enabling precise determination of the population distribution, microwave polarization ratio, and microwave Rabi frequency individually. By analyzing the microwave spectrum, we can track the population distribution while systematically varying the power or period of the optical pumping field(s). In steady-state conditions, our simplified model, which incorporates resonant and off-resonant transitions, reveals an upper limit to the population purity. Through the optimization of the intensity and polarization of the optical pumping field, we have achieved exceptional population purities of up to 96(2)% or 98(1)% for the desired quantum state. These remarkable results indicate a significant advancement in state preparation accuracy. Our all-optical method introduces an approach to achieving high-purity atomic states while employing novel microwave spectroscopy to accurately detect all unknown parameters, offering valuable insights and potential applications in precision measurement and quantum computation research.

Bespoke pulse design for robust rapid two-qubit gates with trapped ions

Two-qubit gate performance is vital for scaling up ion-trap quantum computing. Optimized quantum control is needed to achieve reductions in gate-time and gate error-rate. We describe two-qubit gates with addressed Raman beams within a linear trapped-ion chain by a quantum master equation (QME). The QME incorporates the single-ion two-photon effective Rabi frequency, Autler-Townes and vibrational Bloch-Siegert energy shifts, off-resonant transitions, Raman and Rayleigh scattering, laser-power fluctuations, motional heating, cross-Kerr phonon coupling, laser spillover, asymmetric addressing beams and an imperfect initial motional ground state, with no fitting parameters. Whereas state-of-the-art methods are oblivious to these effects in the gate design procedure. We employ global optimization to design pulse sequences for achieving a robust rapid two-qubit gate for seven trapped $^{171}$Yb$^{+}$ ions by optimizing over numerically integrated QME solutions. Here, robust means resilient against slow drift of motional frequencies, and rapid means gate execution where the effective Rabi frequency is comparable to the detuning of the laser from the ion's bare electronic transition. Our robust quantum control delivers rapid high-quality two-qubit gates in long ion chains, enabling scalable quantum computing with trapped ions.

Effect of fast noise on the fidelity of trapped-ion quantum gates

High-fidelity single- and multiqubit operations compose the backbone of quantum information processing. This fidelity is based on the ability to couple single- or two-qubit levels in an extremely coherent and precise manner. A necessary condition for coherent quantum evolution is a highly stable local oscillator driving these transitions. Here we study the effect of fast noise, that is, noise at frequencies much higher than the local oscillator linewidth, on the fidelity of one- and two-qubit gates in a trapped-ion system. We analyze and measure the effect of fast noise on single-qubit operations, including resonant $\ensuremath{\pi}$ rotations and off-resonant sideband transitions. We further numerically analyze the effect of fast phase noise on the M\o{}lmer-S\o{}rensen two-qubit gate. We find a unified and simple way to estimate the performance of all of these operations through a single parameter given by the noise power spectral density at the qubit response frequency. While our analysis focuses on phase noise and on trapped-ion systems, it is relevant for other sources of fast noise as well as for other qubit systems in which spinlike qubits are coupled by a common bosonic field. Our analysis can help in guiding the design of quantum hardware platforms and gates, improving their fidelity towards fault-tolerant quantum computing.

Sensitive dependence of the linewidth enhancement factor on electronic quantum effects in quantum cascade lasers

The linewidth enhancement factor (LEF) describes the coupling between amplitude and phase fluctuations in a semiconductor laser and has recently been shown to be a crucial component for frequency comb formation in addition to linewidth broadening. It necessarily arises from causality, as famously formulated by the Kramers–Kronig relation, in media with nontrivial dependence of the susceptibility on intensity variations. While thermal contributions are typically slow, and thus can often be excluded by suitably designing the dynamics of an experiment, the many quantum contributions are harder to separate. In order to understand and, ultimately, design the LEF to suitable values for frequency comb formation, soliton generation, or narrow laser linewidth, it is, therefore, important to systematically model all these effects. In this comprehensive work, we introduce a general scheme for computing the LEF, which we employ with a nonequilibrium Green's function model. This direct method, based on simulating the system response under varying optical intensity and extracting the dependence of the susceptibility to intensity fluctuations, can include all relevant electronic effects and predicts the LEF of an operating quantum cascade laser to be in the range of 0.1–1, depending on laser bias and frequency. We also confirm that many-body effects, off-resonant transitions, dispersive (Bloch) gain, counter-rotating terms, intensity-dependent transition energy, and precise subband distributions all significantly contribute and are important for accurate simulations of the LEF.

Picosecond ion-qubit manipulation and spin-phonon entanglement with resonant laser pulses

Ultrafast spin-phonon entanglement based on spin-dependent momentum kicks (SDKs) provides an approach to realize fast entangling gates with intrinsic robustness and scalability for trapped ion quantum computing. Such SDKs so far have been implemented on a nanosecond timescale by off-resonant Raman transitions where each laser pulse is split into a sequence of perturbation pulses with carefully designed temporal patterns. Here we report an experimental realization of ultrafast qubit manipulation and spin-phonon entanglement in picoseconds using SDKs from single resonant laser pulses on the magnetic-field-insensitive hyperfine qubit states. This experiment demonstrates a convenient approach to ultrafast SDKs on noise-insensitive ion-spin qubits, with improvement in its speed by more than an order of magnitude. It removes the need to engineer the pattern of a sequence of perturbation pulses and is less vulnerable to noise, simplifying the approach to large-scale trapped-ion quantum computing based on fast quantum gates with SDKs.

The qutrit as a heat diode and circulator

We investigate the heat transport properties of a three-level system coupled to three thermal baths, assuming a model based on superconducting circuit implementations. The system-bath coupling is mediated by resonators which serve as frequency filters for the different qutrit transitions. Taking into account the finite quality factors of the resonators, we find thermal rectification and circulation effects not expected in configurations with perfectly-filtered couplings. Heat leakage in off-resonant transitions can be exploited to make the system work as an ideal diode where heat flows in the same direction between two baths irrespective of the sign of the temperature difference, as well as a perfect heat circulator whose state is phase-reversible.

High-fidelity quantum gates in Si/SiGe double quantum dots

Motivated by recent experiments of Zajac et al. [arXiv:1708.03530], we theoretically describe high-fidelity two-qubit gates using the exchange interaction between the spins in neighboring quantum dots subject to a magnetic field gradient. We use a combination of analytical calculations and numerical simulations to provide the optimal pulse sequences and parameter settings for the gate operation. We present a novel synchronization method which avoids detrimental spin flips during the gate operation and provide details about phase mismatches accumulated during the two-qubit gates which occur due to residual exchange interaction, non-adiabatic pulses, and off-resonant driving. By adjusting the gate times, synchronizing the resonant and off-resonant transitions, and compensating these phase mismatches by phase control, the overall gate fidelity can be increased significantly.

Ionic dynamics underlying strong-field dissociative molecular ionization

We study strong-field molecular ionization, with a focus on indirect ionization to dissociative excited ionic states. Indirect ionization, also known as post-ionization excitation, refers to the excitation of the molecular cation following ionization to a lower-lying state. We propose two possible mechanisms underlying indirect ionization: resonant transitions facilitated by nuclear dynamics and nonadiabatic transitions driven by the laser field off resonance. We compare them by measuring the dependence of the indirect ionization yield on pulse duration for cations with different electronic structures. Both experiments and simulations confirm the importance of nuclear dynamics in indirect ionization and indicate the presence of off-resonant nonadiabatic transitions.

The nonmonotonous shift of quantum plasmon resonance and plasmon-enhanced photocatalytic activity of gold nanoparticles.

The surface plasmon resonance (SPR) of metal nanoparticles exhibits quantum behaviors as the size decreases owing to the transitions of quantized conduction electrons, but most studies are limited to the monotonous SPR blue-shift caused by off-resonant transitions. Here, we demonstrate the nonmonotonous SPR red-shift caused by resonant electron transitions and photocatalytic activity enhanced by the quantum plasmon resonance of colloidal gold nanoparticles. A maximal SPR wavelength and the largest photocatalytic activity are observed in the quantum regime for the first time for the gold nanoparticles with a diameter of 3.6 nm. Theoretical analysis based on a quantum-corrected model reveals the evolution of SPR with quantized electron transitions and well explains the nonmonotonous size-dependencies of the SPR wavelength and absorption efficiency. These findings have profound implications for the understanding of the quantum nature of the SPR of metal nanoparticles and their applications in areas ranging from photophysics to photochemistry.

Transfer of optical orbital angular momentum to a bound electron.

Photons can carry angular momentum, not only due to their spin, but also due to their spatial structure. This extra twist has been used, for example, to drive circular motion of microscopic particles in optical tweezers as well as to create vortices in quantum gases. Here we excite an atomic transition with a vortex laser beam and demonstrate the transfer of optical orbital angular momentum to the valence electron of a single trapped ion. We observe strongly modified selection rules showing that an atom can absorb two quanta of angular momentum from a single photon: one from the spin and another from the spatial structure of the beam. Furthermore, we show that parasitic ac-Stark shifts from off-resonant transitions are suppressed in the dark centre of vortex beams. These results show how light's spatial structure can determine the characteristics of light–matter interaction and pave the way for its application and observation in other systems.

Fast optical cooling of a nanomechanical cantilever by a dynamical Stark-shift gate.

The efficient cooling of nanomechanical resonators is essential to exploration of quantum properties of the macroscopic or mesoscopic systems. We propose such a laser-cooling scheme for a nanomechanical cantilever, which works even for the low-frequency mechanical mode and under weak cooling lasers. The cantilever is coupled by a diamond nitrogen-vacancy center under a strong magnetic field gradient and the cooling is assisted by a dynamical Stark-shift gate. Our scheme can effectively enhance the desired cooling efficiency by avoiding the off-resonant and undesired carrier transitions, and thereby cool the cantilever down to the vicinity of the vibrational ground state in a fast fashion.

Factorization with a logarithmic energy spectrum of a two-dimensional potential

We propose a method to factor numbers using a single particle caught in a separable two-dimensional potential with a logarithmic energy spectrum. The particle initially prepared in the ground state is excited with high probability by a sinusoidally time-dependent perturbation into a state whose two quantum numbers represent the factors of a number encoded in the frequency of the perturbation. We discuss the limitations of our method arising from off-resonant transitions and from decoherence.

Double Bragg diffraction: A tool for atom optics

The use of retro-reflection in light-pulse atom interferometry under microgravity conditions naturally leads to a double-diffraction scheme. The two pairs of counterpropagating beams induce simultaneously transitions with opposite momentum transfer that, when acting on atoms initially at rest, give rise to symmetric interferometer configurations where the total momentum transfer is automatically doubled and where a number of noise sources and systematic effects cancel out. Here we extend earlier implementations for Raman transitions to the case of Bragg diffraction. In contrast with the single-diffraction case, the existence of additional off-resonant transitions between resonantly connected states precludes the use of the adiabatic elimination technique. Nevertheless, we have been able to obtain analytic results even beyond the deep Bragg regime by employing the so-called "method of averaging," which can be applied to more general situations of this kind. Our results have been validated by comparison to numerical solutions of the basic equations describing the double-diffraction process.

Off-resonant transitions in the collective dynamics of multi-level atomic ensembles

We study the contributions of off-resonant transitions to the dynamics of a system of N multi-level atoms sharing one excitation and interacting with the quantized vector electromagnetic field. The rotating wave approximation significantly simplifies the derivation of the equations of motion describing the collective atomic dynamics, but it leads to an incorrect expression for the dispersive part of the atom–atom interaction terms. For the case of two-level atoms and a scalar electromagnetic field, it turns out that the atom–atom interaction can be recovered correctly if integrals over the photon mode frequencies are extended to incorporate negative values. We explicitly derive the atom–atom interaction for multi-level atoms, coupled to the full vector electromagnetic field, and we recover also in this general case the validity of the results obtained by the extension to negative frequencies of the formulas derived with the rotating wave approximation.

Factorization with a logarithmic energy spectrum

We propose a method to factor numbers based on the quantum dynamics of two interacting bosonic atoms where the single-particle energy spectrum depends logarithmically on the quantum number. We show that two atoms initially prepared in the ground state are preferentially excited by a time-dependent interaction into a two-particle energy state characterized by the factors. Hence, a measurement of the energy of one of the two atoms yields the factors. The number to be factored is encoded in the frequency of a sinusoidally modulated interaction. We also discuss the influence of off-resonant transitions and the limitation of the number to be factored imposed by experimental conditions.

Controllable operation for distant qubits in a two-dimensional quantum network

We propose a theoretical scheme to realize the coherent coupling of multiple atoms in a quantum network which is composed of a two-dimensional (2D) array of coupled cavities. In the scheme, the pairing off-resonant Raman transitions of different atoms, induced by the cavity modes and external fields, can lead to selective coupling between arbitrary atoms trapped in separated cavities. Based on this physical mechanism, quantum gates between any pair of qubits and parallel two-qubit operations can be performed in the 2D system. The scheme provides a new perspective for coherent manipulation of quantum systems in 2D quantum networks.

Controllable coupling of distributed qubits within a microtoroidal cavity network

We propose a scheme to control the coupling between two arbitrary atoms scattered within a quantum network composed of microtoroidal cavities linked by a ring-fibre. The atom-atom effective couplings are induced by pairing of off-resonant Raman transitions. The couplings can be arbitrarily controlled by adjusting classical fields. Compared with the previous scheme [S.B. Zheng, C.P. Yang, F. Nori, Phys. Rev. A 82, 042327 (2010)], the present scheme uses microtoroidal cavities with higher coupling efficiency than Fabry-Perot cavities. Furthermore, the scheme is not only suitable for the short-fibre limit, but also for multiple fibre modes. The added fibre modes can play a positive role, especially when the coupling rate between cavity-mode and fibre-mode is not large. In addition, a wider frequency domain of fibre modes can be used in this scheme.

Quantum State Transfer via the Selective Pairing of off-Resonant Raman Transitions

A simple scheme for transferring an unknown atomic state based on the pairing of off-resonant Raman transitions is proposed. The scheme is insensitive to the atomic spontaneous emission, cavity decay, and fiber decay. Meanwhile, in the scheme, operations between any pair of atomic qubits and selective parallel two-qubit operations on different qubit pairs can be implemented. The atoms, the cavity modes and the fiber are not excited during the operations. A quantum communication net- work for transferring quantum information can be established. Therefore the scheme would be a useful step toward future scalable quantum computing networks.

The single quantum dot-laser: lasing and strong coupling in the high-excitation regime

The emission properties of a single quantum dot in a microcavity are studied on the basis of a semiconductor model. As a function of the pump rate of the system we investigate the onset of stimulated emission, the possibility to realize stimulated emission in the strong-coupling regime, as well as the excitation-dependent changes of the photon statistics and the emission spectrum. The role of possible excited charged and multi-exciton states, the different sources of dephasing for various quantum-dot transitions, and the influence of background emission into the cavity mode are analyzed in detail. In the strong coupling regime, the emission spectrum can contain a line at the cavity resonance in addition to the vacuum doublet caused by off-resonant transitions of the same quantum dot. If strong coupling persists in the regime of stimulated emission, the emission spectrum near the cavity resonance additionally grows due to broadened contributions from higher rungs of the Jaynes-Cummings ladder.

Multidimensional pump-probe spectroscopy with entangled twin-photon states.

We show that entangled photons may be used in coherent multidimensional nonlinear spectroscopy to provide information on matter by scanning photon wave function parameters (entanglement time and delay of twin photons), rather than frequencies and time delays, as is commonly done with classical pulses. Signals are expressed and interpreted intuitively in terms of products of matter and field correlation functions using a diagrammatic close time path loop formalism which reveals the entangled quantum pathways of the fields and matter. The pump-probe signal measured when the pump and the probe are in a twin entangled state shows two-photon resonant contributions which scale linearly rather than quadratically with the incident beam intensity and reveal frequencies of off-resonant transitions. Two-dimensional spectrograms obtained by double Fourier transform of the signal with respect to the entanglement time and delay of the twins could provide detailed information on correlations among states and dynamical processes with high temporal resolution. The analogy with multidimensional time-domain optical techniques which use sequences of short classical pulses and pulse shaping algorithms is pointed out.