Rabi Resonance Research Articles

Nonlinear phenomena in time-dependent density-functional theory: What Rabi oscillations can teach us

Through the exact solution of a two-electron system interacting with a monochromatic laser we prove that all adiabatic density functionals within time-dependent density-functional theory are not able to discern between resonant and non-resonant (detuned) Rabi oscillations. This is rationalized in terms of a fictitious dynamical exchange-correlation (xc) detuning of the resonance while the laser is acting. The non-linear dynamics of the Kohn-Sham system shows the characteristic features of detuned Rabi oscillations even if the exact resonant frequency is used. We identify the source of this error in a contribution from the xc-functional to the non-linear equations describing the electron dynamics in an effective two-level system. The constraint of preventing the detuning introduces a new strong condition to be satisfied by approximate xc-functionals.

Junction fabrication by shadow evaporation without a suspended bridge

We present a novel shadow evaporation technique for the realization of junctionsand capacitors. The design by e-beam lithography of strongly asymmetricundercuts on a bilayer resist enables in situ fabrication of junctions and capacitorswithout the use of the well-known suspended bridge (Dolan 1977 Appl. Phys.Lett. 31 337–9). The absence of bridges increases the mechanical robustnessof the resist mask as well as the accessible range of the junction size, from10 − 2 µm2 to more than104 µm2. We havefabricated Al/AlOx/Al Josephson junctions, phase qubit and capacitors using a 100 kV e-beam writer. Althoughthis high voltage enables a precise control of the undercut, implementation using aconventional 20 kV e-beam is also discussed. The phase qubit coherence times, extractedfrom spectroscopy resonance width, Rabi and Ramsey oscillation decays and energyrelaxation measurements, are longer than the ones obtained in our previous samplesrealized by standard techniques. These results demonstrate the high quality of the junctionobtained by this bridge-free technique.

Raman-assisted Rabi resonances in two-mode cavity QED

The dynamics of a vibronic system in a lossy two-mode cavity is studied, with the first mode being resonant to the electronic transition and the second one being nearly resonant due to Raman transitions. We derive analytical solutions for the dynamics of this system. For a properly chosen detuning of the second mode from the exact Raman resonance, we obtain conditions that are closely related to the phenomenon of Rabi resonance as it is well known in laser physics. Such resonances can be observed in the spontaneous emission spectra, where the spectrum of the second mode in the case of weak Raman coupling is enhanced substantially.

Entanglement of three-mode light via six-wave mixing in a four-level Y-type atomic system

In this paper, we show that it is possible to achieve continuous-variable entanglement of three optical fields in a four-level Y-type atomic system. The three fields are amplified through the Rabi resonances of the different driven transitions. Two fields from the V configuration are in one quantum beat and in the mixing parametric interactions with the third field from the lower transition. This yields entanglement between the pair of beat modes and the third field. The best achievable state in the output approaches the Einstein–Podolsky–Rosen entangled state.

Thermalization of coupled atom-light states in the presence of optical collisions

The interaction of a two-level atomic ensemble with a quantized single mode electromagnetic field in the presence of optical collisions (OC) is investigated both theoretically and experimentally. The main accent is made on achieving thermal equilibrium for coupled atom-light states (in particular dressed states). We propose a model of atomic dressed state thermalization that accounts for the evolution of the pseudo-spin Bloch vector components and characterize the essential role of the spontaneous emission rate in the thermalization process. Our model shows that the time of thermalization of the coupled atom-light states strictly depends on the ratio of the detuning and the resonant Rabi frequency. The predicted time of thermalization is in the nanosecond domain and about ten times shorter than the natural lifetime at full optical power in our experiment. Experimentally we are investigating the interaction of the optical field with rubidium atoms in an ultra-high pressure buffer gas cell under the condition of large atom-field detuning comparable to the thermal energy in frequency units. In particular, an observed detuning dependence of the saturated lineshape is interpreted as evidence for thermal equilibrium of coupled atom-light states. A significant modification of sideband intensity weights is predicted and obtained in this case as well.

Low-velocity limits of cold-atom clocks

Fundamental low-energy limits to the accuracy of quantum clock and stopwatch models in which the clock hand motion is activated by the presence of a particle in a region of space have been studied in the past, but their relevance for actual atomic clocks had not been assessed. In this work we address the effect of slow atomic quantum motion on Rabi and Ramsey resonance fringe patterns, as a perturbation of the results based on classical atomic motion. We find the dependence of the fractional error of the corresponding atomic clocks on the atomic velocity and interaction parameters.

Effects of atomic motion in a standing-wave laser field on the Rabi oscillations

We study the effects of the two-level-atom motion in a standing-wave laser field on the Rabi oscillations. In the presence of the resonance optical Stern–Gerlach effect, the atomic wave packet, centered initially at a node of the standing wave, is shown to evolve in such a way that the atomic population inversion remains zero when the initially de-excited atom moves between the nodes, then collapses to the ground level upon crossing the nodes, and practically returns to zero after that. This coherent population trapping is explained in the dressed-state picture. The Doppler–Rabi resonance, i.e., maximum Rabi oscillations at large values of the atom–field detuning, becomes possible if the detuning is equal to the Doppler shift. A simple formula for the population inversion is derived in the Raman–Nath approximation.

Leakage of the Josephson flux qubit

We study the dynamics of the Josephson flux qubit, which consists on a SQUID loop with three Josephson junctions operated at or near a magnetic flux of half quantum. We perform simulations of the time dependent Schrödinger equation when the system is started in the ground state. The leakage from the two lowest energy levels of the qubit computational subspace to higher energy levels is calculated, when pulses in the magnetic field are applied. We obtain, as expected, that constant field pulses have a higher leakage than rf field pulses at the resonant Rabi frequency. In the case of the constant field pulse we study the average leakage as a function of the pulse intensity, fp. For low fp we obtain that the leakage is quadratic in fp and we compare with a perturbative calculation.

Optimal control of a leaking qubit

Physical implementations of quantum bits can contain coherent transitions to energetically close nonqubit states. In particular, for inharmonic-oscillator systems such as the superconducting phase qubit and the transmon, a two-level approximation is insufficient. We apply optimal control theory to the envelope of a resonant Rabi pulse in a qubit in the presence of a single weakly off-resonant leakage level. The gate error of a spin-flip (NOT) operation reduces by orders of magnitude compared to simple pulse shapes. Near-perfect gates can be achieved for any pulse duration longer than an intrinsic limit given by the nonlinearity. The pulses can be understood as composite sequences that refocus the leakage transition. We also discuss ways to improve the pulse shapes.

Nonlinear response of the vacuum Rabi resonance

The exploration of the Jaynes–Cummings Hamiltonian in a circuit-QED system—where an ‘artificial atom’ made of a superconducting circuit is strongly coupled to a microwave field—provides direct evidence for nonlinearities due to quantum mechanics on the level of single atoms and photons. On the level of single atoms and photons, the coupling between atoms and the electromagnetic field is typically very weak. By using a cavity to confine the field, the strength of this interaction can be increased by many orders of magnitude, to a point where it dominates over any dissipative process. This strong-coupling regime of cavity quantum electrodynamics1,2 has been reached for real atoms in optical cavities3, and for artificial atoms in circuit quantum electrodynamics4 and quantum dot systems5,6. A signature of strong coupling is the splitting of the cavity transmission peak into a pair of resolvable peaks when a single resonant atom is placed inside the cavity, an effect known as vacuum Rabi splitting. The circuit quantum electrodynamics architecture is ideally suited for going beyond this linear-response effect. Here, we show that increasing the drive power results in two unique nonlinear features in the transmitted heterodyne signal: the supersplitting of each vacuum Rabi peak into a doublet and the appearance of extra peaks with the characteristic spacing of the Jaynes–Cummings ladder. These findings constitute direct evidence for the coupling between the quantized microwave field and the anharmonic spectrum of a superconducting qubit acting as an artificial atom.

Coherent optical manipulations of the fundamental state in a single quantum dot

By means of an original all-optical experimental technique using microphotoluminescence in a waveguiding geometry, resonant coherent manipulation of quantum states in a single quantum dot becomes possible now. Resonant Rabi oscillation of the fundamental exciton state in a single quantum dot has been realized. We present the results obtained on two different kinds of samples: InAs/GaAs self-assembled quantum dots and naturally formed GaAs quantum dots by thickness fluctuations.

Dynamics of a Rabi oscillation under a pulsed perturbation

We study how a Rabi oscillation is affected by a periodic pulsed perturbation. Unlike a continuous perturbation, which simply shifts the resonance frequency, a pulsed perturbation splits the Rabi resonance into two lines separated by the pulse repetition rate. When the perturbation integrated over one pulse is equal to $\ensuremath{\pi}$, the resonance splits into two symmetrically placed lines at \ifmmode\pm\else\textpm\fi{} half the pulse repetition rate. When it is $2\ensuremath{\pi}$, the Rabi oscillation is unaffected by the perturbation. We demonstrate these behaviors using the ground hyperfine transition of cesium atoms in a magneto-optical trap. The pulsed perturbation is introduced by a periodic magnetic field pulse. The $2\ensuremath{\pi}$ case is compared with the self-induced transparency, and its implications for optical frequency metrology using a pulsed optical trap is discussed.

Vibronic Rabi resonances in harmonic and hard-wall ion traps for arbitrary laser intensity and detuning

We investigate laser-driven vibronic transitions of a single two-level atomic ion in harmonic and hard-wall traps. In the Lamb-Dicke regime, for tuned or detuned lasers with respect to the internal frequency of the ion, and weak or strong laser intensities, the vibronic transitions occur at well-isolated Rabi resonances, where the detuning-adapted Rabi frequency coincides with the transition frequency between vibrational modes. These vibronic resonances are characterized as avoided crossings of the dressed levels (eigenvalues of the full Hamiltonian). Their peculiarities due to symmetry constraints and trapping potential are also examined.

Electromagnetic Gyration: -- Hamiltonian Dynamics of the Stokes Parameters --

Starting with a Schrodinger-type equation derived from the Maxwell theory of electro- magnetism, a general formalism is presented for the change of light polarization in nonlinear birefringent media, which we call gyration or more generally, electromagnetic gyration and applications are considered. The theory is formulated in terms of the Hamil- tonian dynamics of the Stokes parameters which turns out to be the equation for a classical spin. As applications, we consider two models: (a) As the first application, we analyze solvable models admitting analytic solutions, which exhibit the structure change in the be- havior of the Stokes parameter caused by the mutual interplay between linear and nonlinear birefringence. (b) The second application is the optical analogue of the so-called nuclear magnetic resonance (NMR) or Rabi resonance. This is investigated in the case of purely linear birefringence and coexisting of linear and nonlinear birefringence.

Laser excitation of transverse modes in an atomic waveguide

We investigate the effect of a laser shining perpendicularly to a waveguide channeling two-level atoms. For weak transversal coupling the excitation of transverse atomic levels occurs at avoided crossings associated with "Rabi resonances" in which the Rabi frequency coincides with the transition frequency between the transverse levels.

Inapplicability of the giant oscillator strength model to excitonic molecule in an inorganic‐organic layered semiconductor

AbstractThe author reports the measurement of the resonant Rabi splitting of the transition between the exciton and the excitonic molecule in an inorganic‐organic layered semiconductor, (C6H13C2H4NH3)2PbI4. The transition dipole moment is determined to be 3.5 ± 0.4 eÅ. It is shown that the obtained transition dipole moment is considerably smaller than that estimated from the well‐known giant oscillator strength model. The discrepancy between the experiment and the model is explained to be due to the strong polaritonic effect. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Theory of the microwave spectroscopy of a phosphorus-donor charge qubit in silicon: Coherent control in theSi:Pquantum-computer architecture

We present a theoretical analysis of a microwave spectroscopy experiment on a charge qubit defined by a ${\mathrm{P}}_{2}^{+}$ donor pair in silicon, for which we calculate Hamiltonian parameters using the effective-mass theory of shallow donors. The master equation of the driven system in a dissipative system is solved to predict experimental outcomes. We describe how to calculate physical parameters of the system from such experimental results, including the dephasing time, ${T}_{2}$, and the ratio of the resonant Rabi frequency to the relaxation rate. Finally we calculate probability distributions for experimentally relevant system parameters for a particular fabrication regime.

Comparative short-term stability for a Cs beam and an expanding cold atomic cloud of Cs used as atomic frequency standards

We have compared the stability of two distinct atomic frequency standards. One is based on an atomic cold cloud of 133Cs atoms in free expansion, interrogated by a Rabi resonance. The other standard is based on a thermal Cs beam interrogated by the separated oscillatory field method (Ramsey’s method). The atomic expanding cloud standard shows better stability and technical advances based on its simplicity.

Nuclear spin state narrowing via gate-controlled Rabi oscillations in a double quantum dot

We study spin dynamics for two electrons confined to a double quantum dot under the influence of an oscillating exchange interaction. This leads to driven Rabi oscillations between the $\ket{\uparrow\downarrow}$--state and the $\ket{\downarrow\uparrow}$--state of the two--electron system. The width of the Rabi resonance is proportional to the amplitude of the oscillating exchange. A measurement of the Rabi resonance allows one to narrow the distribution of nuclear spin states and thereby to prolong the spin decoherence time. Further, we study decoherence of the two-electron states due to the hyperfine interaction and give requirements on the parameters of the system in order to initialize in the $\ket{\uparrow\downarrow}$--state and to perform a $\sqrt{\mathrm{SWAP}}$ operation with unit fidelity.

Floquet scattering approach to electron transport for a quantum wire under longitudinallypolarized electromagnetic field irradiation

We theoretically study the electron transport property for a semiconductor quantum wireirradiated under a longitudinally polarized electromagnetic field within a finite range. Weobtain the non-perturbative solutions of the single-electron time-dependent Schrödingerequation both inside and outside the field-irradiated region of the wire according tothe Floquet theorem. A general infinite matrix equation which determines theFloquet scattering coefficients is derived straightforwardly through the wavefunctionmatching scheme at the two interfaces between regions with and without fieldirradiation. The examples of numerically calculated transmission dependenceon the electron incident energy for different field parameters exhibit both Fanoand Rabi resonances, and the structure of the transmission is sensitive to thefield parameters of amplitude and frequency as well as the irradiation length.