Pulse Area Theorem Research Articles

Pulse-area theorem for precision control of the rotational motions of a single molecule in a cavity

We perform a combined analytical and numerical investigation to explore how an analytically designed pulse can precisely control the rotational motions of a single-molecular polariton formed by the strong coupling of two low-lying rotational states with a single-mode cavity. To this end, we derive a pulse-area theorem that gives amplitude and phase conditions of the pulses in the frequency domain for driving the polariton from a given initial state to an arbitrary coherent state. The pulse-area theorem is examined for generating the maximum degree of orientation using a pair of pulses. We show that the phase condition can be satisfied by setting the initial phases of the two identically overlapped pulses or by controlling the time delay between pulses for practical applications.

Self-induced transparency in a semiconductor quantum dot medium at ultracold temperatures

We investigate the feasibility of minimum absorption and minimum broadening of pulse propagation in an inhomogeneously broadened semiconductor quantum dot medium. The phonon interaction is inevitable in studying any semiconductor quantum dot system. We have used the polaron transformation technique to deal with quantum dot phonon interaction in solving system dynamics. We demonstrate that a short pulse can propagate inside the medium with minimal absorption and broadening in pulse shape. The stable pulse area becomes slightly higher than the prediction of the pulse area theorem and is also dependent on the environment temperature. The change in the final pulse shape is explained very well by numerically solving the propagation equation supported by the susceptibility of the medium. Our system also exhibits the pulse breakup phenomena for higher input pulse areas. Therefore, the considered scheme can have important applications in quantum communication, quantum information, and mode-locking with the advantage of scalability and controllability.

Photon/spin echo in a Fabry-Perot cavity.

The pulse area theorem is a well-known versatile analytical tool for capturing the general nonlinear nature of light propagation in a two-level medium. Here we derive the pulse area theorem for the photon/spin echo signal generated in a one-side cavity. The obtained analytical solutions for primary and secondary echo pulse areas allow us to describe the nonlinear patterns of the photon/spin echo signals in an atomic ensemble in a cavity. The developed approach and the obtained results constitute an important step in the study of the general properties of the photon/spin echo in optical and microwave cavities expanding applications of the photon echo in coherent spectroscopy, quantum memory, and processing.

Two-pulse photon echo area theorem in an optically dense medium.

We perform a theoretical and experimental study of the two-pulse photon echo area conservation law in an optically dense medium. The experimental properties of the echo signal are studied at 4K on the optical transition 3H6(1)→3H4(1) (793 nm) of Tm3+ in a YAG crystal for a wide range of pulse areas of the two incoming light pulses, up to θ 1 r o x4π and θ 2≈7π respectively, with optical depth 1.5. We analyze the experimental data by using the analytic solution of the photon echo area theorem for plane waves. We find that the transverse Gaussian spatial profile of the beam leads to an attenuation of the echo area nutation as function of θ1 and θ2. Additional spatial filtering of the photon echo beam allows to recover this nutation. The experimental data are in good agreement with the solution of photon echo pulse area theorem for weak incoming pulse areas θ 1,2≲π. However at higher pulse areas, the observations diverge from the analytic solution requiring further theoretical and experimental studies.

All-optical generation of quantum entangled states with strictly constrained ultrafast laser pulses

We present a quantum optimal control theory study combined with theoretical analysis to determine a pulsed laser field, capable of generating a maximally entangled state in two trapped two-level atoms. By expanding the time-dependent unitary operator to the first leading term of Magnus expansion, we reexamine the pulse area theorem for the trapped atoms driven by an arbitrarily temporary field. Due to the dipole-dipole interaction blockade, we find that the two trapped atoms described by a three-level ladder system can be reduced into an equivalent two-level model by using narrow-bandwidth pulses, leading to an analytical solution for generating the maximally entangled state. We also solve a highly constrained optimization problem to search for optimal laser pulses with broad bandwidths. A zero pulse-area constraint is employed to remove the dc offset of the optimized laser pulses, and a fixed fluence limitation combined with a constant pulse-area constraint at the resonant frequency of the equivalent two-level system are utilized to restrict the unitary evolution of quantum systems by the first leading term of Magnus expansion. This work provides a potentially useful approach to find all-optical control schemes for generating the maximally entangled state by using ultrafast laser pulses while satisfying multiple strict limitations.

Fast quantum state transfer in hybrid quantum dot-metal nanoparticle systems by shaping ultrafast laser pulses

Semiconductor quantum dots (SQDs) have relatively short decoherence times, but have the potential for extremely fast operations implemented by femto-second laser pulses, making them a possible candidate for very high speed quantum information processing. These operations are enhanced by positioning a metal nano-particle (MNP) near to the SQD which significantly increases the strength of electric fields applied to it. Here we consider an SQD with three-levels in a Lambda configuration, and explore the requirements for implementing a transfer from one ground state to the other via the upper level. A recently developed optimization method allows us to fix the energy of the laser pulse while satisfying the requirement that the pulse has no DC component. We show that the use of carefully shaped pulses significantly reduces the required laser power. We also determine the dependence of the pulse power on the distance between the SQD and the MNP, and explore the degree to which the process follows the pulse area theorem for first-order perturbative processes.

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.

Development of weak coherent 0π optical pulses in a ring resonator with a dynamic recurrent loop

We investigated the development of weak coherent 0π optical pulses in a ring resonator with a dynamic recurrent loop. Using this recurrent system, we measured transmitted pulse profiles as a function of the recurrence time, that is, the number of times pulses passed through the resonator. As the number increased, the transmitted pulse profiles developed oscillating structures characteristic of weak coherent 0π optical pulses. The pulse area decayed exponentially to 0π, independent of the pulse duration and pulse shape, thus obeying the pulse area theorem described by McCall and Hahn in the linear regime. The fact that the pulse area decays exponentially does not necessarily imply that the pulses lose their energy. Successful observation of the coherent 0π pulses demonstrated the potential application of the system to a wide variety of experiments in which pulse states are examined after passing through resonators of exactly the same resonance frequency, with an ultrahigh Q-value, an arbitrary number of times.

Analytic solution and pulse area theorem for three-level atoms

We report an analytic solution for a three-level atom driven by arbitrary time-dependent electromagnetic pulses. In particular, we consider far-detuned driving pulses and show an excellent match between our analytic result and the numerical simulations. We use our solution to derive a pulse area theorem for three--level $V$ and $\Lambda$ systems without making the rotating wave approximation. Formulated as an energy conservation law, this pulse area theorem provides a simple picture for a pulse propagation through a three--level media.

Fundamental limit to qubit control with coherent field

The ultimate accuracy as regards controlling a qubit with a coherent field is studied in terms of degradation of the fidelity by employing a fully quantum mechanical treatment. While the fidelity error accompanied by pi/2 pulse control is shown to be inversely proportional to the average photon number in a way similar to that revealed by the Gea-Banacloche's results. Our results show that the error depends strongly on the initial state of the qubit. When the initial state of the qubit is in the ground state, the error is about 20 times smaller than that of the control started from the exited state, no matter how large N is. This dependency is explained in the context of an exact quantum mechanical description of the pulse area theorem. By using the result, the error accumulation tendency of successive pulse controls is found to be both non-linear and initial state-dependent.

Effect of laser pulse shaping parameters on the fidelity of quantum logic gates

The effect of varying parameters specific to laser pulse shaping instruments on resulting fidelities for the ACNOT(1), NOT(2), and Hadamard(2) quantum logic gates are studied for the diatomic molecule (12)C(16)O. These parameters include varying the frequency resolution, adjusting the number of frequency components and also varying the amplitude and phase at each frequency component. A time domain analytic form of the original discretized frequency domain laser pulse function is derived, providing a useful means to infer the resulting pulse shape through variations to the aforementioned parameters. We show that amplitude variation at each frequency component is a crucial requirement for optimal laser pulse shaping, whereas phase variation provides minimal contribution. We also show that high fidelity laser pulses are dependent upon the frequency resolution and increasing the number of frequency components provides only a small incremental improvement to quantum gate fidelity. Analysis through use of the pulse area theorem confirms the resulting population dynamics for one or two frequency high fidelity laser pulses and implies similar dynamics for more complex laser pulse shapes. The ability to produce high fidelity laser pulses that provide both population control and global phase alignment is attributed greatly to the natural evolution phase alignment of the qubits involved within the quantum logic gate operation.

Beyond the pulse-area theorem: Role of the absorption and the dispersion in the propagation of weak ultrashort resonant pulses

We present here some fundamental but yet underlooked features of the propagation of weak ultrashort pulses (with Δ d τ << 1, where Δ d is the Doppler width and τ is the pulse duration) in resonant atomic media. We show that the pulse area behaviour and the pulse spectrum at resonance are governed by the usual optical depth ( α 0 L, where α 0 is the absorption coefficient at resonance and L the length of the medium), whereas the pertinent parameter that governs the severity of the dispersion effects and the distortion of the pulse is the dispersion parameter e disp = ( α 0 L) Δ d τ that we introduce. Paradoxical effect such as distortionless propagation (e.g. e disp << 1) with vanishing pulse area (when α 0 L >> 1) can then explained within this formalism.

Quantum computing based on vibrational eigenstates: Pulse area theorem analysis

In a recent paper [D. Babikov, J. Chem. Phys. 121, 7577 (2004)], quantum optimal control theory was applied to analyze the accuracy of quantum gates in a quantum computer based on molecular vibrational eigenstates. The effects of the anharmonicity parameter of the molecule, the target time of the pulse, and the penalty function on the accuracy of the qubit transformations were investigated. We demonstrate that the effects of all the molecular and laser-pulse parameters can be explained utilizing the analytical pulse area theorem, which originates from the standard two-level model. Moreover, by analyzing the difference between the optimal control theory results and those obtained using the pulse area theorem, it is shown that extremely high quantum gate fidelity can be achieved for a qubit system based on vibrational eigenstates.

Propagation and amplification of ultrashort light pulses in a resonant two-level medium: finite-difference time-domain analysis

Propagation and amplification of an ultrashort laser pulse in a two-level medium is numerically investigated with the use of the finite-difference time-domain (FDTD) procedure simultaneously solving Maxwell and Schrödinger equations with no assumptions characteristic of slowly varying envelope approximation. Comparison of the results of FDTD numerical simulations with the predictions of the pulse area theorem has demonstrated that the developed numerical procedure provides an adequate description of pulse evolution in a two-level medium. Amplification of ultrashort light pulses in a two-level medium is analyzed. Two methods of improving the gain of ultrashort pulses in a two-level medium by modulating the spatial distribution of dipole moments of resonant transitions and using initially chirped frequency-detuned pulses are explored.

Transient pulse propagation and pulse break-up phenomena in III–V semiconductors

The coherent radition-semiconductor interaction model based upon the time-dependent perturbation technique has been employed for the analytical study of transient pulse propagation and pulse break-up in directgap semiconductors. In order to check the validity of our model, we have applied our analysis initially to the Rubidium atomic vapor system duly irradiated with pulsed ruby laser. Numerical estimation of the change in transient transmitted intensity reveals good agreement between the present results and the experimental observations in Rb vapor system. Finally, we have analyzed pulse propagation in an important direct-gap crystal, namely InSb duly irradiated by ultrafast infrared dye laser operating in the 3.9-9.4 μm wavelength range. Pulse break-up and pulse peak shifts can be noticed from the results. The pulse velocity is also found to reduce by at least a factor of 100. These features are analogous to the phenomenon of self-induced transparency where the pulse area theorem is usually employed.

Switching dynamics of spatial solitary wave pixels

Separatrices and scaling laws in the switching dynamics of spatial solitary wave pixels are investigated. We show that the dynamics in the full model are similar to those in the plane-wave limit. Switching features may be indicated and explained by the motion of the (complex) solitary wave amplitude in the phase plane. We report generalization, into the domain of transverse effects, of the pulse area theorem for the switching process and a logarithmic law for the transient dynamics. We also consider, for what is the first time to our knowledge, phase-encoded address of solitary pixels and find that a near-square-wave temporal switching pattern is permitted without (transverse) cross switching.

Oscillatory free-induction decay signals in the angular distribution of nuclear radiation in ferromagnetic metals under strong inhomogeneous broadening

The problem of the oscillatory free induction decay in the angular distribution of nuclear radiations is theoretically examined for inhomogeneous linewidths, with and without the influence of the skin effect, utilizing the method of concatenation of perturbation factors. The second rank detection tensor applicable to gamma detected pulsed NMRON signals from ferromagnetic metals is examined for axial geometry. Important extensions to the pulse area theorem originally developed only for the first rank detection tensor are proposed for second rank tensors.