A simple theoretical solution to the design of a control field that generates complete population transfer from an initial state, via $N$ nondegenerate intermediate states, to one arbitrary member of $M$ ($M\leq N$) degenerate states is constructed. The full control field exploits an $(M+N-1)$-node null adiabatic state, created by designing the relative phases and amplitudes of the component fields that together make up the full field. The solution found is universal in the sense that it does not depend on the exact number of the unwanted degenerate states or their properties. The results obtained suggest that a class of multi-level quantum systems with degenerate states can be completely controllable, even under extremely strong constraints, e.g., never populating a Hilbert subspace that is only a few dimensions smaller than the whole Hilbert space.
We find a set of conditions to achieve complete population transfer, via coherent population trapping, from an initial state to a designated final state at a designated time in a degenerate n-state atom, where the transitions are caused by an external interaction.
We find conditions required to achieve complete population transfer, via coherent population trapping, from an initial state to a designated final state at a designated time in a degenerate $n$-state atom, where transitions are caused by an external interaction. In systems with degenerate states there is no time ordering. Analytic expressions have been found for transition probabilities in a degenerate $n$-state atom interacting with a strong external field that gives a common time dependence to all of the transition matrix elements. Except for solving a simple $n^{th}$ order equation to deter…
A five-level four-pulse phase-sensitive extended stimulated Raman adiabatic passage scheme is proposed to realize complete control of the population transfer branching ratio between two degenerate target states. The control is achieved via a three-node null eigenstate that can be correlated with an arbitrary superposition of the target states. Our results suggest that complete suppression of the yield of one of two degenerate product states, and therefore absolute selectivity in photochemistry, is achievable and predictable, even without studying the properties of the unwanted product state be…
We find conditions required to achieve complete population transfer, via coherent population trapping, from an initial state to a designated final state at a designated time in a degenerate 3-level atom, where transitions are caused by an external interaction. Complete population transfer from an initially occupied state 1 to a designated state 2 occurs under two conditions. First, there is a constraint on the ratios of the transition matrix elements of the external interaction. Second, there is a constraint on the action integral over the interaction, or "area", corresponding to the phase shi…
We consider the time evolution of nearly degenerate two-state systems with an external interaction. Conditions in which full population transfer is possible when the two-states become degenerate are considered. A new variation of the coupled differential equations for the probability amplitudes suggests a possible singularity in the time evolution of the system. The singularity occurs at the point in time where full control in the degenerate limit is achieved. We solve this new variation to derive more information about non-degenerate population control. The new results of numerical calculatio…
The interaction of a three level Rydberg atom of Lambda-type with a single mode optical field in far off-resonant and at large detuning regimes can be described by an effective degenerate Raman model, where the atomic state can be treated as a two-level system of degenerate states. By means of this approximation, we propose a quantum information transfer of an one-qubit state from a Rydberg atom of Lambda-type with degenerate levels to a single-mode field initially in a coherent state.
Spectroscopic features revealing the coherent interaction of a degenerate two-level atomic system with two optical fields are examined. A model for the numerical calculation of the response of a degenerate two-level system to the action of an arbitrarily intense resonant pump field and a weak probe in the presence of a magnetic field is presented. The model is valid for arbitrary values of the total angular momentum of the lower and upper levels and for any choice of the polarizations of the optical waves. Closed and open degenerate two-level systems are considered. Predictions for probe absor…
We prove complete controllability for rotational states of an asymmetric top molecule belonging to degenerate values of the orientational quantum number M. Based on this insight, we construct a pulse sequence that energetically separates population initially distributed over degenerate M-states, as a precursor for orientational purification. Introducing the concept of enantio-selective controllability, we determine the conditions for complete enantiomer-specific population transfer in chiral molecules and construct pulse sequences realizing this transfer for population initially distributed ov…
For a transition $F_e=0\leftrightarrow F_g=1$ driven by a linearly polarized light and probed by a circularly light, quantum coherence effects are investigated. Due to the coherence between the drive Rabi frequency and Zeeman splitting, electromagnetically induced transparency, electromagnetically induced absorption, and the transition from positive to negative dispersion are obtained, as well as the populations coherently oscillating in a wide spectral region. At the zero pump-probe detuning, the subluminal and superluminal light propagation is predicted. Finally, coherent population trapping…
A model for the information transfer from DNA to protein using quantum information and computation techniques is presented. DNA is modeled as the sender and proteins are modeled as the receiver of this information. On the DNA side, a 64-dimensional Hilbert space is used to describe the information stored in DNA triplets (codons). A Hamiltonian matrix is constructed for this space, using the 64 possible codons as base states. The eigenvalues of this matrix are not degenerate. The genetic code is degenerate and proteins comprise only 20 different amino acids. Since information is conserved, the …
A novel effect of population transfer in a five-level system is analyzed. This population transfer effect is found to be a version of a Raman process, which is facilitated and assisted by coherence effects, acting to close other available decay channels.
We examine the conditions needed to accomplish stimulated Raman adiabatic passage (STIRAP) when the three levels (g, e and f) are degenerate, with arbitrary couplings contributing to the pump-pulse interaction (g - e) and to the Stokes-pulse interaction (e-f). We show that in general a sufficient condition for complete population removal from the g set of degenerate states for arbitrary, pure or mixed, initial state is that the degeneracies should not decrease along the sequence g, e and f. We show that when this condition holds it is possible to achieve the degenerate counterpart of conventio…
In this paper, a method to accelerate population transfer by designing nonadiabatic evolution paths is proposed. We apply the method to realize robust and accelerated population transfer with a transmon qutrit. By numerical simulation, we show that this method allows a robust population transfer between the ground states in a $Λ$ system. Moreover, the total pulse area for the population transfer is low as 1.9$π$ that verifies the evolution is accelerated without increasing the pulse intensity. Therefore, the method is easily implementable based on the modern pulse shaper technology and it prov…
We propose an asymmetric double quantum well structure with a common continuum and investigate the effect of resonant tunneling on the control of coherent electron population transfer between the two quantum wells. By numerically solving the motion equations of element moments, the almost complete electron population transfer from initial subband to the target subband could be realized due to the constructive interference via flexibly adjusting the structure parameters.
Stimulated Raman adiabatic passage is a well-known technique for quantum population transfer due to its robustness again various sources of noises. Here we consider quantum population transfer from one spin to another via an intermediate spin which subjects to dephasing noise. We obtain an analytic expression for the transfer efficiency under a specific driving protocol, showing that dephasing could reduce the transfer efficiency, but the effect of dephasing could also be suppressed with a stronger laser coupling or a longer laser duration. We also consider another commonly used driving protoc…
For a two-level system, it is believed that a far-off-resonant driving can not help coherent population transfer between the states. In this work, we propose a scheme to implement the coherent transfer with far-off-resonant driving. The scheme works well with both constant driving and Gaussian driving. The total time to finish population transfer is also minimized by optimizing the detuning and coupling constants. We find that the scheme is sensitive to spontaneous emission much more than dephasing. It might find potential applications in X-ray quantum optics and population transfer in Rydberg…
There has long been interest to control the transfer of population between specified quantum states. Recent work has optimized the control law for closed system population transfer by using a gradient ascent pulse engineer- ing algorithm [1]. Here, a spin-boson model consisting of two-level atoms which interact with the dissipative environment, is investigated. With opti- mal control, the quantum system can invert the populations of the quantum logic states. The temperature plays an important role in controlling popula- tion transfer. At low temperatures the control has active performance, whi…
Atomic population transfer in an inhomogeneously broadened optical medium is analyzed for on-demand photon storage-time control in both atomic frequency comb (AFC) and phase locked echoes. In AFC the photon storage mechanism belongs to the conventional three-pulse photon echoes, while the storage time control is limited by conventional two-pulse photon echoes.
We design, by invariant-based inverse engineering, resonant laser pulses to perform fast population transfers in three-level systems. The efficiency and laser intensities are examined for different protocols. The energy cost to improve the fidelity is quantified. The laser intensities can be reduced by populating the intermediate state and by multi-mode driving.
We propose a model to study quantum population transfer via a structural continuum. The model is composed of two spins which are coupled to two bosonic modes separately by two control pulses, and the two bosonic modes are coupled to a common structural continuum. We show that efficient population transfer can be achieved between the two spins by using a multi-level stimulated Raman adiabatic passage (STIRAP) across the continuum, which we refer to as straddle STIRAP via continuum. We also consider the stability of this model against different control parameters and show that efficient populati…
We examine the stability of population transfer in two- and three-level systems against unwanted additional transitions. This population inversion is achieved by using recently proposed schemes called "shortcuts to adiabaticity". We quantify and compare the sensitivity of different schemes to these unwanted transitions. Finally, we provide examples of shortcut schemes which lead to a zero transition sensitivity in certain regimes, i.e. which lead to a nearly perfect population inversion even in the presence of unwanted transitions.
High-fidelity and robust coherent population transfer is a major challenge in coherent quantum control. Different from the well known adiabatic condition, we present a rigorous adiabatic condition that is inspired by the idea of the Landau-Zener tunneling. Based on this, we propose a coherent population transfer approach, which just needs only one control parameter and depends on the eigenvalues of the systems. Compared to other approaches, such as fast quasiadiabatic dynamics, shortcut to adiabatic passage, we numerically demonstrate that our approach can provide a more high-fidelity and more…
Accurate population transfer of uncoupled or weakly coupled spin states is crucial for many quantum information processing tasks. In this paper, we propose a fast and robust scheme for population transfer which combines invariant-based inverse engineering and geometric formalism for robust quantum control. Our scheme is not constrained by the adiabatic condition and therefore can be implemented fast. It can also effectively suppress the dominant noise in spin systems, which together with the fast feature guarantees the accuracy of the population transfer. Moreover, the control parameters of th…
We describe a relation between the requirement of complete population transfer in a four-mode system and the generating function of Pythagorean triples from number theory. We show that complete population transfer will occur if ratios between coupling coefficients exactly match one of the Pythagorean triples (a; b; c) in Z, c^{2} = a^{2} + b^{2}. For a four-level ladder system this relation takes a simple form (V12; V23; V34) ~ (c; b; a), where coefficients Vij describe the coupling between modes. We find that the structure of the evolution operator and the period of complete population transf…
Formulas for transverse conductance in quantum non-degenerate collisional plasma are deduced. The kinetic equation in momentum space in the relaxation approach is used. It is shown, that at $\hbar\to 0$ the derived formula transfers to the classical one. It is shown also, that when values of dimensionless wave numbers are small, the conductance formula transfers in the known formula for classical non-degenerate plasmas.
An automated and robust method for adiabatic population transfer and the preparation of an arbitrary quantum superposition state in atomic system using the oscillating dark states (ODS) is presented. Quantum state of a three-level $Λ$ configuration atomic system oscillates periodically between two ground levels, when two pairs of classical detuning laser fields driving the system into the ODS under evolving adiabatic conditions. The decoherence of the ODS evolution is greatly suppressed, and the oscillation is very stable, therefore adiabatic population transfer and the preparation of an arbit…
We demonstrate a method of adiabatic population transfer from a single quantum state into a coherent superposition of states. The transfer is executed with femtosecond pulses, spectrally shaped in simple and intuitive manner, which does not require iterative feedback-controlled loops. In contrast to non-adiabatic methods of excitation, our approach is not sensitive to the exact value of laser intensity. We show that the population transfer is complete, and analyze the possibility of controlling the relative phases and amplitudes of the excited eigenstates. We discuss the limitations of the pro…
We propose a class of schemes for robust population transfer between quantum states that utilize trains of coherent pulses and represent a generalized adiabatic passage via a wave packet. We study piecewise Stimulated Raman Adiabatic Passage with pulse-to-pulse amplitude variation, and piecewise chirped Raman passage with pulse-to-pulse phase variation, implemented with an optical frequency comb. In the context of production of ultracold ground-state molecules, we show that with almost no knowledge of the excited potential, robust high-efficiency transfer is possible
In the previous paper on this topic it was shown how, for a pulse of arbitrary shape and duration, the drive frequency can be analytically optimized to maximize the amplitude of the population oscillations between the selected two levels in a general many level quantum system. It was shown how the standard Rabi theory can be extended beyond the simple two-level systems. Now, in order to achieve the quickest and as complete as possible population transfer between two pre-selected levels, driving pulse should be tailored so that it produces only a single half-oscillation of the population. In th…
We develop a mathematically rigorous theory for the quantum transfer processes in degenerate donor-acceptor dimers in contact with a thermal environment. We calculate explicitly the transfer rates and the acceptor population efficiency. The latter depends critically on the initial donor state. We show that quantum coherence in the initial state enhances the transfer process. If the electron is initially shared coherently by the donor levels then the efficiency can reach values close to 100%, while an incoherent initial donor state will significantly suppress the efficiency. The results are use…
The Toffoli gate is an essential logic element, which permits implementation of a reversible processor. It is of relevance both for classical as well as quantum logics. We propose and theoretically study all-optical implementations of three-bit and four-bit Toffoli gates by application of adiabatic population transfer techniques. For a three-bit Toffoli gate we use variants of stimulated Raman adiabatic passage (STIRAP) processes in a $Λ$-type level scheme, driven by two laser pulses at sufficiently large detunings. For the implementation of a four-bit Toffoli gate, we apply reversible adiabat…
Population transfer in quantum systems has always been an interesting area in physics since the introduction of quantum mechanics. In this paper, transition probabilities for a coupled system consisting of four two - level particles are studied by solving Landau - Zener Hamiltonian. The effects of the first and second nearest neighbors interactions are investigated. Presented results indicate that the second nearest neighbors interactions will decrease the transition probability when the coupling strength for each neighborhood has the same sign. The fast sweep effect on transition probability …
State selective preparation and manipulation of discrete-level quantum systems such as atoms, molecules or quantum dots is a the ultimate tool for many diverse fields such as laser control of chemical reactions, atom optics, high-precision metrology and quantum computing. Rabi oscillations are one of the simplest, yet potentially quite useful mechanisms for achieving such manipulation. Rabi theory establishes that in the two-level systems resonant drive leads to the periodic and complete population oscillations between the two system levels. In this paper an analytic optimization algorithm for…
Achieving fast populations transfer (FPT) in multiparticle systems based on the cavity quantum electronic dynamics (CQED) is an outstanding challenge. In this paper, motivated by the quantum Zeno dynamics (QZD), a shortcut for performing the FPT of ground states in multiparticle systems with the invariant based inverse engineering is proposed. Numerical simulation demonstrates that a perfect populations transfer of ground states in multiparticle systems can be rapidly achieved in one step, and the FPT is robust to both the cavity decay and atomic spontaneous emission. Additionally, this scheme…
Transferring the state of a quantum system to a given distribution of populations is an important problem with applications to Quantum Chemistry and Atomic Physics. In this work we consider exact population transfers that minimize the L^2 norm of the control which is typically the amplitude of an electromagnetic field. This problem is analytically and numerically challenging. Except for few exactly solvable cases, there is no general understanding of the nature of optimal controls and trajectories. We find that by examining the limit of large transfer times, we can uncover such general propert…
We show that the physical mechanism of population transfer in a 3-level system with a closed loop of coherent couplings (loop-STIRAP) is not equivalent to an adiabatic rotation of the dark-state of the Hamiltonian but coresponds to a rotation of a higher-order trapping state in a generalized adiabatic basis. The concept of generalized adiabatic basis sets is used as a constructive tool to design pulse sequences for stimulated Raman adiabatic passage (STIRAP) which give maximum population transfer also under conditions when the usual condition of adiabaticty is only poorly fulfilled. Under cert…
The influence of photon-momentum recoil on adiabatic population transfer in an atomic three-level lambda system is studied. It is shown that the Doppler frequency shifts, due to atomic motion can play an important role in adiabatic population transfer processes of atomic internal states by a pair of laser fields. For the limiting case of slow atoms ( Doppler shift much smaller than the photon recoil energy) the atoms occupy the same target state regardless of the order of switching of laser fields, while for the case of fast atoms interacting with the intuitive sequence of pulses, the target s…
We consider the optimal control problem of transferring population between states of a quantum system where the coupling proceeds only via intermediate states that are subject to decay. We pose the question whether it is generally possible to carry out this transfer. For a single intermediate decaying state, we recover the Stimulated Raman Adiabatic Passage (STIRAP) process which we identify as the global optimum in the limit of infinite control time. We also present analytic solutions for the case of transfer that has to proceed via two consecutive intermediate decaying states. We show that i…
We report studies of state-to-state vibrational energy transfer in an isolated polyatomic molecule driven by combined stimulated Raman adiabatic passage (STIRAP) and counter-diabatic fields (CDF), using as vehicles selective population of one of a pair of near degenerate states in SCCl$_2$ and enhancing the yield of HNC in the HCN/HNC isomerization reaction. The efficiency of the population transfer within a subset of states embedded in a dense manifold of states is examined for the cases that the transition dipole moments between the initial and target states are much smaller than and compara…
We use the approach of "transitionless quantum driving" proposed by Berry to construct shortcuts to the population transfer and the creation of maximal entanglement between two $Λ$-type atoms based on the cavity quantum electronic dynamics (CQED) system. An effective Hamiltonian is designed by resorting to an auxiliary excited level, a classical driving field and an extra cavity field mode to supplement or substitute the original reference Hamiltonian, and steer the system evolution along its instantaneous eigenstates in an arbitrarily short time, speeding up the rate of population transfer an…
We consider the dynamics of a single electron in a chain of tunnel coupled quantum dots, exploring the formal analogies of this system with some of the laser-driven multilevel atomic or molecular systems studied by Bruce W. Shore and collaborators over the last 30 years. In particular, we describe two regimes for achieving complete coherent transfer of population in such a multistate system. In the first regime, by carefully arranging the coupling strengths, the flow of population between the states of the system can be made periodic in time. In the second regime, by employing a "counterintuit…
A technique for complete population transfer between the two end states $\ket{1}$ and $\ket{3}$ of a three-state quantum system with a train of $N$ pairs of resonant and coincident pump and Stokes pulses is introduced. A simple analytic formula is derived for the ratios of the pulse amplitudes in each pair for which the maximum transient population $P_2(t)$ of the middle state $\ket{2}$ is minimized, $P_2^{\max}=\sin^2(π/4N)$. It is remarkable that, even though the pulses are on exact resonance, $P_2(t)$ is damped to negligibly small values even for a small number of pulse pairs. The populatio…
Formulas for transverse conductance in quantum collisional plasma are deduced. The kinetic equation in momentum space in the relaxation approach is used. It is shown, that at Planck's constant tends to zero the derived formula transfers to the classical one. It is shown also, that when electron collision frequency tends to null (i.e. plasma becomes collisionless), the conductance formula transfers in the known formula inferred earlier by Lindhard.
We study quantum control techniques, specifically Adiabatic Rapid Passage (ARP) and Gradient Ascent Pulse Engineering (GRAPE), for transferring atoms trapped in an optical lattice between different vibrational states. We compare them with each other and with previously studied coupling schemes in terms of performance. In our study of ARP, we realize control of the vibrational states by tuning the frequency of a spatial modulation through the inhomogeneously broadened vibrational absorption spectrum. We show that due to the presence of multiple crossings, the population transfer depends on the …
We propose a simple exact analytical solution for a model consisting of a two-level system and a polychromatically driving field. It helps us to realize a rapid complete population transfer from the ground state to the excited state, and the system can be stable at the excited state for an extremely long time. A combination of the mechanism and the Rydberg atoms successfully prepares the Bell state and multipartite $W$ state, and the experimental feasibility is discussed via the current experimental parameters. Finally, the simple exact analytical solution is generalized into a three-level sys…
Fine control of the dynamics of a quantum system is the key element to perform quantum information processing and coherent manipulations for atomic and molecular systems. In this paper we propose a control protocol using a tangent-pulse driven model and demonstrate that it indicates a desirable design, i.e., of being both fast and accurate for population transfer. As opposed to other existing strategies, a remarkable character of the present scheme is that high velocity of the nonadiabatic evolution itself not only will not lead to unwanted transitions but also can suppress the error caused by…
In this work, we propose a composite pulses scheme by modulating phases to achieve high fidelity population transfer in three-level systems. To circumvent the obstacle that not enough variables are exploited to eliminate the systematic errors in the transition probability, we put forward a cost function to find the optimal value. The cost function is independently constructed either in ensuring an accurate population of the target state, or in suppressing the population of the leakage state, or both of them. The results demonstrate that population transfer is implemented with high fidelity eve…
We study quantum population transfer via a common intermediate state initially in thermal equilibrium with a finite temperature $T$, exhibiting a multi-level Stimulated Raman adiabatic passage structure. We consider two situations for the common intermediate state, namely a discrete two-level spin and a bosonic continuum. In both cases we show that the finite temperature strongly affects the efficiency of the population transfer. We also show in the discrete case that strong coupling with the intermediate state, or a longer duration of the controlled pulse would suppress the effect of finite t…
We develop a method for executing robust and selective transfer of populations between a single level and pre-selected superpositions of energy eigenstates. Viewed in the frequency domain, our method amounts to executing a series of simultaneous adiabatic passages into each component of the target superposition state. Viewed in {the} time domain, the method works by accumulating the wavefunction of the target wave packet as it revisits the Franck Condon region, in what amounts to an extension of the Piecewise Adiabatic Passage technique [ Shapiro et.al., Phys. Rev. Lett. 99, 033002 (2007)] to …
We study the dynamics of a two-level quantum system under the influence of sinusoidal driving in the intermediate frequency regime. Analyzing the Floquet quasienergy spectrum, we find combinations of the field parameters for which population transfer is optimal and takes place through a series of well defined steps of fixed duration. We also show how the corresponding evolution operator can be approximated at all times by a very simple analytical expression. We propose this model as being specially suitable for treating periodic driving at avoided crossings found in complex multi-level systems…
We design, by invariant-based inverse engineering, driving fields that invert the population of a two-level atom in a given time, robustly with respect to dephasing noise and/or systematic frequency shifts. Without imposing constraints, optimal protocols are insensitive to the perturbations but need an infinite energy. For a constrained value of the Rabi frequency, a flat $π$ pulse is the least sensitive protocol to phase noise but not to systematic frequency shifts, for which we describe and optimize a family of protocols.
Shortcut to adiabaticity in various quantum systems has attracted much attention with the wide applications in quantum information processing and quantum control. In this paper, we concentrate on stimulated Raman shortcut-to-adiabatic passage in quantum three-level systems. To implement counter-diabatic driving but without additional coupling, we first reduce the quantum three-level systems to effective two-level problems at large intermediate-level detuning, or on resonance, apply counter-diabatic driving along with the unitary transformation, and eventually modify the pump and Stokes pulses …
We report theoretical studies of adiabatic population transfer using dressed spin states. Quantum optimal control using the algorithm of Chopped Random Basis (CRAB) has been implemented in a negatively charged diamond nitrogen vacancy center that is coupled to a strong and resonant microwave field. We show that the dressed spin states are highly effective in suppressing effects of spin dephasing on adiabatic population transfer. The numerical simulation also demonstrates that CRAB-based quantum optimal control can enable an efficient and robust adiabatic population transfer.
The Stimulated Raman Adiabatic Passage (STIRAP) procedure is a robust and complete population transfer method which have various application in chemistry and atomic physics. Here, we study the effects of one-photon detuning, transition time, pulse width, and pulse delay parameters on the population transfer via STIRAP and b-STIRAP techniques. Moreover, the impact of the field amplitude which decreases the population transfer has been analyzed and it is shown that in b-STIRAP, the robustness of the complete transition can be improved by decreasing the field amplitude in the single-photon resona…
