Complete Population Inversion Research Articles

Birefringent Spin‐Photon Interface Generates Polarization Entanglement

AbstractA spin‐photon interface based on the luminescence of a singly charged quantum dot in a micropillar cavity allows for the creation of photonic entangled states. Current devices suffer from cavity birefringence, which limits the generation of spin‐photon entanglement. In this study, we conduct a theoretical analysis of the light absorption and emission by the interface with an anisotropic cavity and derive the maximal excitation and spin‐photon entanglement conditions. It is shown that the concurrence of the spin‐photon state equal to one and complete quantum dot population inversion can be reached for a micropillar cavity with any degree of birefringence by tuning the quantum dot resonance strictly between the cavity modes. This sweet spot is also valid for generating a multiphoton cluster state, as demonstrated by calculating the three‐tangle and fidelity with the maximally entangled state.

Excited quantum anomalous and spin Hall effect: dissociation of flat-bands-enabled excitonic insulator state

Quantum anomalous Hall effect (QAHE) and quantum spin Hall effect (QSHE) are two interesting physical manifestations of 2D materials that have an intrinsic nontrivial band topology. In principle, they are ground-state equilibrium properties characterized by Fermi level lying in a topological gap, below which all the occupied bands are summed to a non-zero topological invariant. Here, we propose theoretical concepts and models of ‘excited’ QAHE (EQAHE) and EQSHE generated by dissociation of an excitonic insulator (EI) state with complete population inversion (CPI), a unique many-body ground state enabled by two yin-yang flat bands (FBs) of opposite chirality hosted in a diatomic Kagome lattice. The two FBs have a trivial gap in between, i.e. the system is a trivial insulator in the single-particle ground-state, but nontrivial gaps above and below, so that upon photoexcitation the quasi-Fermi levels of both electrons and holes will lie in a nontrivial gap achieved by the CPI-EI state, as demonstrated by exact diagonalization calculations. Then dissociation of singlet and triplet EI state will lead to EQAHE and EQSHE, respectively. Realizations of yin-yang FBs in real materials are also discussed.

Trajectory tracking for non-Markovian quantum systems

We propose a systematic scheme to engineer quantum states of a quantum system governed by a time-convolutionless non-Markovian master equation. According to the idea of reverse engineering, the general algebraic equation to determine the control parameters, such as coherent and incoherent control fields, is presented. Without artificially engineering the time-dependent decay rates and retaining the environment-induced Lamb shifts, the quantum state can still be transferred into the target state in a finite period of time along an arbitrary designed trajectory strictly in Hilbert space. As an application, we apply our scheme to a driven two-level non-Markovian system and realize instantaneous-steady-state tracking and a complete population inversion with control parameters which are available in experimental settings.

Complete population inversion of maximally entangled states in 22N -level systems via Pythagorean-triple coupling

Maximally entangled states play a central role in quantum information processing. Despite much progress throughout the years, robust protocols for manipulations of such states in many-level systems are still scarce. Here we present a control scheme that allows efficient manipulation of complete population inversion between two maximally entangled states. Exploiting the self-duality of $\mathrm{SU}(2)$, we present in this work a family of ${2}^{2N}$-level systems with couplings related to Pythagorean triples that make a complete population inversion from one state to another (orthogonal) state, using very few couplings and generators. We relate our method to the recently developed retrograde-canon scheme and derive a more general complete transfer recipe. We also discuss the cases of ${(2n)}^{2}$-level systems, ${(2n+1)}^{2}$-level systems, and other unitary groups, and give a geometrical description of the inversion via the Majorana sphere.

Quantum sensing of weak electric and magnetic fields by coherent amplification of energy-level-shift effects

A method for measuring small energy level shifts in a qubit by coherent amplification of their effect is proposed. It is based on the repeated application of the same interaction pulse in two manners: with the same phase of each subsequent pulse, and with an alternating phase shift of $\pi$ (i.e. a minus sign) from pulse to pulse. Two specific types of pulses are considered: a resonant $\pi$ pulse and an adiabatic chirped pulse, both of which produce complete population inversion with high fidelity. In the presence of a weak ambient external electric or magnetic field, the ensuing Stark or Zeeman shift leads to an energy level shift and hence a static detuning. In both the resonant and adiabatic approaches, a small level shift does not alter the transition probability very much; however, it can significantly change the dynamical phases in the propagator. The repeated application of the same pulse greatly amplifies the changes in the dynamical phases and maps them onto the populations. Hence the effect of the level shift can be measured with good accuracy. It is found that sequences of pulses with alternating phases deliver much greater error amplification and much steeper excitation profiles around resonance, thereby providing much higher sensitivity to small energy level shifts. Explicit analytic estimates of the sensitivity are derived using the well-known non-crossing Rosen-Zener and Rabi models and the level-crossing Demkov-Kunike model. This recipe provides a simple tool for rapid and accurate sensing of weak electric and magnetic fields by using the same pulse generating an inversion quantum gate, without sophisticated tomography or entangling operations.

Population transfer in a nonlinear three-level Λ-system by Stark - chirped rapid adiabatic passage

We propose the use of the Stark-chirped rapid adiabatic passage (SCRAP) method to induce a complete population transfer in a nonlinear three-level Λ-type system (nl-SCRAP). We also use the nl-SCRAP method for creating stable diatomic ground molecular Bose–Einstein condensates (BECs) from atomic BECs. In this three-laser technique the pump and Stokes pulses are slightly detuned from transition frequencies, and a third strong hyperbolic-tangent laser pulse induces dynamic Stark shifts of the relevant transitions and compensates for third-order nonlinearities. If the timing of the three pulses is appropriately chosen, the nonlinear quantum system is prepared to almost complete population inversion between the two lower states in the Λ-like scheme. The paper shows that the efficiency of the nl-SCRAP is higher than the nonlinear stimulated Raman adiabatic passage (nl-STIRAP) technique, and this method can be used in one-photon as well as multi-photon transitions. The transfer process is robust concerning fluctuations of experimental parameters, such as peak Rabi frequencies, the time delay between pulses, and static detunings.

Unidirectional quantum transport in optically driven V -type quantum dot chains

We predict a mechanism for achieving complete population inversion in a continuously driven InAs/GaAs semiconductor quantum dot featuring $V$-type transitions. This highly nonequilibrium steady state is enabled by the interplay between $V$-type interband transitions and a non-Markovian decoherence mechanism, introduced by acoustic phonons. The population trapping mechanism is generalized to a chain of coupled emitters. Exploiting the population inversion, we predict unidirectional excitation transport from one end of the chain to the other without external bias, independent of the unitary interdot coupling mechanism.

Effective pulse reverse-engineering for strong field-matter interaction.

In this Letter, we propose a scheme to control the evolution of a two-level quantum system in the strong-coupling regime, based on the idea of reverse engineering. A coherent control field is designed to drive the system along a user-predefined evolution trajectory without utilizing the rotating-wave approximation. As concrete examples, we show that complete population inversion, an equally weighted coherent superposition, and even oscillation-like dynamics can be achieved. Since there are no limitations on the coupling strength between the control field and matter, the scheme is attractive for applications such as accelerating desired system dynamics and fast quantum information processing.

Excitation probability of the hyperfine ground state of Doppler-broadened muonic hydrogen through dipole-forbidden transition

We study the magnetic dipole induced excitation probability of the hyperfine ground state of Doppler-broadened muonic hydrogen (pμ−) by a single nanosecond laser pulse with pulse durations of 20, 2, and 0.2 ns pulses with a Gaussian temporal shape such that the pulse bandwidth is, respectively, narrower than, comparable to, and broader than the Doppler width at 300 K. We numerically solve a set of density matrix equations to obtain the excitation probability at the various laser intensities and detunings. For the resonant 20 ns pulse, the excitation probability increases very slowly as the laser intensity increases. The width of the excitation probability lineshape mainly comes from the Doppler broadening and hardly increases with intensity. For the resonant 0.2 ns pulse a complete population inversion occurs at a certain laser intensity, and the excitation probability oscillates between 0 and unity as the intensity further increases. Owing to the inherent pulse bandwidth the width of the excitation probability lineshape is very broad even at the low intensity, and it increases further as the intensity increases. For the resonant 2 ns pulse at a moderate intensity (∼1011 W/cm2) the excitation probability is higher than those by the 20 and 0.2 ns pulses with a relatively narrow width. Our study can serve as a guideline for the development of the relevant laser source, depending on the purpose to excite muonic hydrogen, i.e., precise measurement of the ground state hyperfine splitting of muonic hydrogen or production of spin-polarized muonic hydrogen.

Steady-state population inversion of multiple Ξ -type atoms by the squeezed vacuum in a waveguide

We study the dynamics of multiple $\mathrm{\ensuremath{\Xi}}$-type atoms driven by a squeezed vacuum reservoir in a quasi-one-dimensional waveguide. We show that the atomic system's steady state is a pure state, and a complete population inversion can occur when the dipole moment of the second transition is almost perpendicular to the polarization of the incident squeezed light. We also prove that the steady state of the system is the direct product of that in the single-atom case with modified squeezed vacuum even when dipole-dipole interaction is involved. This steady-state population inversion may be used to study the two-photon laser or collective atomic effect.

A quantum retrograde canon: complete population inversion in n2-state systems

We present a novel approach for analytically reducing a family of time-dependent multi-state quantum control problems to two-state systems. The presented method translates between related n2-state systems and two-state systems, such that the former undergo complete population inversion (CPI) if and only if the latter reach specific states. For even n, the method translates any two-state CPI scheme to a family of CPI schemes in n2-state systems. In particular, facilitating CPI in a four-state system via real time-dependent nearest-neighbors couplings is reduced to facilitating CPI in a two-level system. Furthermore, we show that the method can be used for operator control, and provide conditions for producing several universal gates for quantum computation as an example. In addition, we indicate a basis for utilizing the method in optimal control problems.

Ultrashort Radiation of Biexcitonic Superfluorescence from High-Density Assembly of Semiconductor Quantum Dots

High-density semiconductor quantum dot (QD) assembly is a promising system to generate ultrashort radiation of superfluorescence (SF) which is a cooperative emission of many coherent excited particles induced by an interaction with a resonant radiation field. In this paper, we report the superfluorescent spectra and time profiles of biexcitons in CuCl QDs where a complete population inversion between the biexciton and exciton states was achieved by resonant two-photon excitation of biexcitons. A spontaneous emission at low excitation density changed to SF by increasing the excitation density. For a high excitation density, superfluorescent characteristics, i.e., narrowing of the pulse width and shortening of the delay time, were observed. Furthermore, broadening of the spectral width was observed, resulting from the enhancement of radiative rate of QD assembly. On the other hand, the SF at low temperature changed to an amplified spontaneous emission with the increase in temperature due to the increase in ...

Analytical results for a parity-time-symmetric two-level system under synchronous combined modulations

We propose a simple method of combined synchronous modulations to generate the analytically exact solutions for a parity-time symmetric two-level system. Such exact solutions are expressible in terms of simple elementary functions and helpful for illuminating some generalizations of appealing concepts originating in the Hermitian system. Some intriguing physical phenomena, such as stabilization of a non-Hermitian system by periodic driving, non-Hermitian analogs of coherent destruction of tunneling (CDT) and complete population inversion (CPI), are demonstrated analytically and confirmed numerically. In addition, by using these exact solutions we derive a pulse area theorem for such non-Hermitian CPI in the parity-time symmetric two-level system. Our results may provide an additional possibility for pulse manipulation and coherent control of the parity-time symmetric two-level system.

Low-power broadband solid-state MAS NMR of 14N.

We propose two broadband pulse schemes for 14N solid-state magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) that achieves (i) complete population inversion and (ii) efficient excitation of the double-quantum spectrum using low-power single-sideband-selective pulses. We give a comprehensive theoretical description of both schemes using a common framework that is based on the jolting-frame formalism of Caravatti et al. [J. Magn. Reson. 55, 88 (1983)]. This formalism is used to determine for the first time that we can obtain complete population inversion of 14N under low-power conditions, which we do here using single-sideband-selective adiabatic pulses. It is then used to predict that double-quantum coherences can be excited using low-power single-sideband-selective pulses. We then proceed to design a new experimental scheme for double-quantum excitation. The final double-quantum excitation pulse scheme is easily incorporated into other NMR experiments, as demonstrated here for double quantum-single quantum 14N correlation spectroscopy, and 1H-14N dipolar heteronuclear multiple-quantum correlation experiments. These pulses and irradiation schemes are evaluated numerically using simulations on single crystals and full powders, as well as experimentally on ammonium oxalate ((NH4)2C2O4) at moderate MAS and glycine at ultra-fast MAS. The performance of these new NMR methods is found to be very high, with population inversion efficiencies of 100% and double-quantum excitation efficiencies of 30%-50%, which are hitherto unprecedented for the low radiofrequency field amplitudes, up to the spinning frequency, that are used here.

Two-level parabolic model with phase-jump coupling

We study the coherent dynamics of a two-level parabolic model and ways to enhance population transfer and even to obtain complete population inversion in such models. Motivated by the complete population inversion effect of zero-area pulses found in [1], we consider a scheme where a given coupling function is transformed to a zero-area coupling by performing phase-jump in the middle of the evolution. We also derive a universal formula for the effect of the phase-jump.

High-fidelity population inversion of two-level system

Population inversion from an initial quantum state to a desired quantum state represents an exciting new frontier for quantum manipulation; that frontier is endowed with a strong interdisciplinary character and connections to other scientific fields, including atomic, molecular, and optical physics, as well as in solid-state devices, for fundamental studies, nuclear magnetic resonance and other spectroscopic techniques, metrology, interferometry, optical control of chemical reactions or quantum-information applications. Two-level systems are ubiquitous in these areas, and the driving of a population inversion is an important operation. So far various schemes for population transfer to a target state from an initial state have been proposed in theory and implemented in experiment. To be useful, such methods must, of course, be reliable, fast, and robust. Most literatures on two-level models investigated population inversion, which could be modelled by infinite-time processes. In this paper, by using a composite adiabatic passage (CAP) technique—in which the single pulse driving the quantum transition is replaced by a sequence of pulses with well-defined control phases, we investigate the population inversion problem of two-level quantum system with a finite duration. We take a sinusoidally varying pulse model that continuously vanishes at the beginning and the end of the finite duration as an example. The high-fidelity population inversion of the two-level system with finite duration is achieved. We discuss the effects of both coupling strength and detuning strength on the transition probability. It is found that this protocol could suppress the oscillations in the transition probability and reduce the admissible error bellow the 10 -4 quantum computation benchmark. The fidelity can arrive at 1, even with simple three- and five-composite pulse sequences. The protocol combines the advantages of adiabatic passage and composite pulses techniques. By choosing the composite phases appropriately, a high-fidelity, fast, stable and extremely robust complete population inversion is achieved for the finite-time two-level model. The values of the composite phases are universal for they do not depend on the pulse shapes and the chirp as long as the latter satisfy the symmetry property. Furthermore, the classical Hamiltonian is applied to describe the dynamic properties of the quantum system and further verify the effectiveness and feasibility of the proposed CAP technique. The results we present here are general and in principle apply to any two- and multi-level quantum systems. The accuracy of the CAP technique and its robustness against parameter variations make the protocol suitable for ultrahigh-fidelity quantum manipulation. We believe that the protocol can be widely used in many different areas of science, ranging from the quantum information, the quantum chemical, and the quantum optics to the ultracold atomic and molecular physics.

Complete population inversion of Bose particles by an adiabatic cycle

We show that an adiabatic cycle excites Bose particles confined in a one-dimensional box. During the adiabatic cycle, a wall described by a δ-shaped potential is applied and its strength and position are slowly varied. When the system is initially prepared in the ground state, namely, in the zero-temperature equilibrium state, the adiabatic cycle brings all Bosons into the first excited one-particle state, leaving the system in a nonequilibrium state. The absorbed energy during the cycle is proportional to the number of Bosons.

Quantum dynamics of a two-state system induced by a chirped zero-area pulse

It is well known that area pulses make Rabi oscillation and chirped pulses in the adiabatic interaction regime induce complete population inversion of a two-state system. Here we show that chirped zero-area pulses could engineer an interplay between the adiabatic evolution and Rabi-like oscillations. In a proof-of-principle experiment utilizing spectral chirping of femtosecond laser pulses with a resonant spectral hole, we demonstrate that the chirped zero-area pulses could induce, for example, complete population inversion and return of the cold rubidium atom two-state system. Experimental result agrees well with the theoretically considered overall dynamics, which could be approximately modeled to a Ramsey-like three-pulse interaction, where the $x$- and $z$- rotations are respectively driven by the hole and the main pulse.

Trichromatic π-Pulse for Ultrafast Total Inversion of a Four-Level Ladder System

We present a numerical solution for complete population inversion in a four-level ladder system obtained by using a full π-pulse illumination scheme with resonant ultrashort phase-locked Gaussian laser pulses. We find that a set of pulse areas such as √3π , √2π , and √3π completely inverts the four-level system considering identical effective dipole coupling coefficients. The solution is consistent provided the involved electric fields are not too strong and it is amply accurate also in the case of diverse transition dipole moments. We study the effect of detuning and chirp of the laser pulses on the complete population inversion using the level structure of atomic sodium interacting with ps and fs pulses as an example. Our result opens the door for multiple applications such as efficient ultrashort pulse lasing in the UV or the engineering of quantum states for quantum computing.

Ultrafast optical switching in quantum dot-metallic nanoparticle hybrid systems.

We study ultrafast excitonic population inversion resulting from the interaction of a semiconductor quantum dot (SQD) with localized surface plasmons. The plasmonic enhanced fields are generated when a metallic nanoparticle (MNP) is subject to a nonlinear chirped few-cycle pulse train. By numerically solving the time-dependent Bloch equations beyond the rotating-wave approximation, we show that the complete population inversion can be achieved for small interparticle distance and the dynamic in population inversion exhibits a steplike transition between absorption and amplifying. This phenomenon can be exploited as an all-optical ultrafast switching device. Moreover, the final state of population inversion is shown to be modified significantly with the interparticle distances, which is not only robust against the variation of probe pulse parameters but also suggests a straightforward method for measuring the interparticle distances via probing the final populations.