### 57622 results for qubit oscillator frequency

Contributors: Whittaker, J. D., da Silva, F. C. S., Allman, M. S., Lecocq, F., Cicak, K., Sirois, A. J., Teufel, J. D., Aumentado, J., Simmonds, R. W.

Date: 2014-08-08

**qubit** lifetimes are relatively large across the full **qubit** spectrum with...**Qubits**...**oscillations** for **frequencies** near f 01 = 7.38 GHz. (b) Line-cut on-resonance...**qubit** anharmonicity, **qubit**-cavity coupling and detuning. A tunable cavity...**qubit** inductively coupled to a single-mode, resonant cavity with a tunable...**qubit** anharmonicity α r versus **qubit** **frequency** ω 01 / 2 π (design A )....**qubit** flux bias is swept. Two different data sets (with the **qubit** reset...**qubit** far detuned, biased at its maximum **frequency**. The solid line is ...**qubit** and cavity **frequencies** and the dashed lines show the new coupled...**qubits**....**qubit** **frequency**, at f 01 = 7.98 GHz, Ramsey **oscillations** gave T 2 * = ...**qubit**-cavity system, we show that dynamic control over the cavity **frequency**...**qubit** anharmonicity as shown later in Fig. Fig9....**qubit** **frequencies**. In order to capture the maximum dispersive **frequency**...**qubit**, and residual bus coupling for a system with multiple **qubits**. With...**qubit** anharmonicity α r versus **qubit** frequency ω 01 / 2 π (design A )....**qubit** evolutions and optimize state readout during **qubit** measurements....**oscillation** decay time of T ' = 409 ns. (c) Ramsey **oscillations** versus...**qubit** is ...**qubit**) (see text)....**qubit** **frequenc**...**qubit** spectrum....**oscillations** gave T ' = 727 ns, a separate measurement of **qubit** energy...**frequency**, f c min ≈ 4.8 GHz. Notice in Fig. Fig6(a) that Rabi **oscillations**...**frequency** provides a way to strongly vary both the **qubit**-cavity detuning...**frequency** that allows for both microwave readout of tunneling and dispersive...**qubit** for various frequencies in order to excite the **qubit** transitions...**qubit** frequency change both Δ 01 and the **qubit**’s anharmonicity α . In ...**qubit** flux detuning near f 01 = 7.38 GHz. (d) Line-cut along the dashed ... We describe a tunable-cavity QED architecture with an rf SQUID phase **qubit** inductively coupled to a single-mode, resonant cavity with a tunable **frequency** that allows for both microwave readout of tunneling and dispersive measurements of the **qubit**. Dispersive measurement is well characterized by a three-level model, strongly dependent on **qubit** anharmonicity, **qubit**-cavity coupling and detuning. A tunable cavity **frequency** provides a way to strongly vary both the **qubit**-cavity detuning and coupling strength, which can reduce Purcell losses, cavity-induced dephasing of the **qubit**, and residual bus coupling for a system with multiple **qubits**. With our **qubit**-cavity system, we show that dynamic control over the cavity **frequency** enables one to avoid Purcell losses during coherent **qubit** evolutions and optimize state readout during **qubit** measurements. The maximum **qubit** decay time $T_1$ = 1.5 $\mu$s is found to be limited by surface dielectric losses from a design geometry similar to planar transmon **qubits**.

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Contributors: Zhirov, O. V., Shepelyansky, D. L.

Date: 2007-10-10

**qubit** coupled to a quantum dissipative driven oscillator (resonator). ...**qubit** polarization with polarization angles θ φ defined in text (right...**qubit** synchronization is illustrated in a more clear way in Fig. fig2...**oscillator** with x = â + â / 2 , p = â - â / 2 i (left) and for **qubit** polarization...**qubit** with radiation suppression at **qubit** frequency Ω = 1.2 ω 0 and appearance...**frequency** of effective Rabi **oscillations** between quasi-degenerate levels...**oscillator** performs circle rotations in p x plane with **frequency** ω while...**qubit** radiation spectrum with appearance of narrow lines corresponding...**qubit** coupled to a driven dissipative oscillator...**qubit** exhibits tunneling between two orientations with a macroscopic change...**qubit** coupled to a driven **oscillator** with jumps between two metastable...**qubit** polarization phase φ vs. oscillator phase ϕ ( p / x = - tan ϕ ) ...**qubit** rotations become synchronized with the oscillator phase. In the ...**qubit** radiation ξ z t as function of driving power n p in presence of ...**qubit** polarization components ξ x and ξ z (full and dashed curves) on ...**qubit** frequency Ω / ω 0 for parameters of Fig. fig1; N f are computed...**qubit** **frequency** Ω / ω 0 for parameters of Fig. fig1; N f are computed...**qubit** polarization phase φ vs. **oscillator** phase ϕ ( p / x = - tan ϕ ) ...**qubit** rotations become synchronized with the **oscillator** phase. In the ...**qubit** with radiation suppression at **qubit** **frequency** Ω = 1.2 ω 0 and appearance...**oscillator** in two metastable states on the driving **frequency** ω (average...**qubit** coupled to a quantum dissipative driven **oscillator** (resonator). ...**qubit** (right) coupled by quantum tunneling (the angles are determined ... We study numerically the behavior of **qubit** coupled to a quantum dissipative driven **oscillator** (resonator). Above a critical coupling strength the **qubit** rotations become synchronized with the **oscillator** phase. In the synchronized regime, at certain parameters, the **qubit** exhibits tunneling between two orientations with a macroscopic change of number of photons in the resonator. The life times in these metastable states can be enormously large. The synchronization leads to a drastic change of **qubit** radiation spectrum with appearance of narrow lines corresponding to recently observed single artificial-atom lasing [O. Astafiev {\it et al.} Nature {\bf 449}, 588 (2007)].

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Contributors: Hua, Ming, Deng, Fu-Guo

Date: 2013-09-30

**qubit**-state-dependent resonator transition, which means the **frequency** ...**qubits** assisted by a resonator in the quasi-dispersive regime with a new...**qubit** q in the transition between the energy levels | i q and | j q ),...**frequency** of two **qubits** between and are chosen as ω 0 , 1 ; 1 / 2 π = ...**qubit** q 1 are taken as ω a / 2 π = 6.0 GHz, ω q 1 / 2 π = 7.0 GHz, and...**qubits** can play an important role in shortening largely the operation ...**oscillations** in our cc-phase gate on a three-charge-**qubit** system. Here...**frequency** shift δ q takes place on the **qubit** due to the photon number ...**qubits**....**frequencies** of the **qubits**....**qubits**, and q 3 is the target **qubit**. The initial state of this system ...three-**qubit** gate, such as a Fredkin gate on a three-**qubit** system can also...**qubit**. (b) The number-state-dependent **qubit** transition, which means the...**qubit**-state-dependent resonator transition, which means the frequency ...**oscillation**, respectively. The MAEV s vary with the transition **frequency**...**frequency** of q 2 (which equals to the transition **frequency** of R a when...**oscillation** varying with the coupling strength g 2 and the **frequency** of...**qubit**, according to Ref. . Here ω r a / 2 π = 6.0 GHz. The transition ...**oscillations** can be suppressed a lot, and the fidelity of this cc-phase...**Qubits** in Circuit QED...**qubit**-state-dependent resonator transition frequency and the tunable period...**qubits**. More interesting, the non-computational third excitation states...**qubits** than previous proposals....**qubit** ω 2 . (a) The outcomes for ROT 0 : | 0 1 | 1 2 | 0 a ↔ | 0 1 | 0...**oscillation** and an unwanted one. This operation does not require any kind...**qubit** and q 2 is the target **qubit**. The initial state of the system composed...**qubit**-state-dependent resonator transition **frequency** and the tunable period...**frequency** on R a becomes ... We present a fast quantum entangling operation on superconducting **qubits** assisted by a resonator in the quasi-dispersive regime with a new effect --- the selective resonance coming from the amplified **qubit**-state-dependent resonator transition **frequency** and the tunable period relation between a wanted quantum Rabi **oscillation** and an unwanted one. This operation does not require any kind of drive fields and the interaction between **qubits**. More interesting, the non-computational third excitation states of the charge **qubits** can play an important role in shortening largely the operation time of the entangling gates. All those features provide an effective way to realize much faster quantum entangling gates on superconducting **qubits** than previous proposals.

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Contributors: Catelani, G., Schoelkopf, R. J., Devoret, M. H., Glazman, L. I.

Date: 2011-06-04

anharmonic **qubit**, such as the transmon and phase qubits. We start with...**qubit**, such as the transmon and phase **qubits**. We start with the the semiclassical...**qubit** controlled by a magnetic flux, see Eq. ( Hphi). (b) Effective circuit...**qubit** biased at Φ e = Φ 0 / 2 with E J / E L = 10 . The horizontal lines.../ 2 **qubit**-quasiparticle coupling in Eq. ( HTle) has a striking effect ...**qubit** sate. The results of Sec. sec:semi are valid for transitions between...**qubit** resonant frequency. In the semiclassical regime of small E C , the...the **qubit** states | - , | + are respectively symmetric and antisymmetric...**qubits**. The interaction of the **qubit** degree of freedom with the quasiparticles...**frequency** [cf. Eq. ( pl_fr)]...**qubit** frequency in the presence of quasiparticles....**frequency** is given by Eq. ( Gnn) with ϕ 0 = 0 and is independent of n ...**qubit** **frequency** in the presence of quasiparticles....**oscillations** of the energy levels are exponentially small, see Appendix...**qubit** resonant **frequency**. In the semiclassical regime of small E C , the...**qubit** properties in devices such as the phase and flux **qubits**, the split...**qubits**...**qubit** can be described by the effective circuit of Fig. fig1(b), with...**frequency** ω p , Eq. ( pl_fr)] and nearly degenerate levels whose energies...**qubit** decay rate induced by quasiparticles, and we study its dependence...**frequency** ω p , Eq. ( pl_fr), and give, for example, the rate Γ 1 0 . ... As low-loss non-linear elements, Josephson junctions are the building blocks of superconducting **qubits**. The interaction of the **qubit** degree of freedom with the quasiparticles tunneling through the junction represent an intrinsic relaxation mechanism. We develop a general theory for the **qubit** decay rate induced by quasiparticles, and we study its dependence on the magnetic flux used to tune the **qubit** properties in devices such as the phase and flux **qubits**, the split transmon, and the fluxonium. Our estimates for the decay rate apply to both thermal equilibrium and non-equilibrium quasiparticles. We propose measuring the rate in a split transmon to obtain information on the possible non-equilibrium quasiparticle distribution. We also derive expressions for the shift in **qubit** **frequency** in the presence of quasiparticles.

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Contributors: Wallraff, A., Schuster, D. I., Blais, A., Frunzio, L., Majer, J., Girvin, S. M., Schoelkopf, R. J.

Date: 2005-02-27

**qubit** population P vs. pulse separation Δ t using the pulse sequence shown...**qubit** state in this setup....**oscillating** at the detuning **frequency** Δ a , s = ω a - ω s ∼ 6 M H z decay...**oscillations** in the **qubit** population P vs. Rabi pulse length Δ t (blue...**oscillation** experiment with a superconducting **qubit** we show that a visibility...**qubit** we show that a visibility in the **qubit** excited state population ...**oscillations** in the **qubit** at a **frequency** of ν R a b i = n s g / π , where...**qubit**. In the 2D density plot Fig. fig:2DRabi, Rabi **oscillations** are ...**qubit** population P is plotted versus Δ t in Fig. fig:rabioscillationsa...**oscillation** **frequency** ν R a b i with the pulse amplitude ϵ s ∝ n s , see...**qubit** excited state population of more than 90 % can be attained. We perform...**Qubit** with Dispersive Readout...**qubit** state by coupling the **qubit** non-resonantly to a transmission line...**qubit**. In each panel the dashed lines correspond to the expected measurement...**oscillations** with Rabi pulse length Δ t , pulse **frequency** ω s and amplitude...**qubit** population P vs. Rabi pulse length Δ t (blue dots) and fit with ...**qubit**, a visibility in the population of the **qubit** excited state that ...**qubit** transition frequency ω a = ω s + 2 π ν R a m s e y ....**oscillations** in a superconducting **qubit**, a visibility in the population...**qubit** coherence time is determined to be larger than 500 ns in a measurement...**oscillator** at **frequency** ω L O . The Cooper pair box level separation is ... In a Rabi **oscillation** experiment with a superconducting **qubit** we show that a visibility in the **qubit** excited state population of more than 90 % can be attained. We perform a dispersive measurement of the **qubit** state by coupling the **qubit** non-resonantly to a transmission line resonator and probing the resonator transmission spectrum. The measurement process is well characterized and quantitatively understood. The **qubit** coherence time is determined to be larger than 500 ns in a measurement of Ramsey fringes.

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Contributors: Chen, Yu, Sank, D., O'Malley, P., White, T., Barends, R., Chiaro, B., Kelly, J., Lucero, E., Mariantoni, M., Megrant, A.

Date: 2012-09-09

**qubits** can be read out simultaneously using **frequency** multiplexing on ...**qubit** in the ground state | g stays in the left well ( L ). (b) Readout...four-**qubit** sample. F B 1 - 4 are control lines for each **qubit** and R R ...**qubits** used in Ref. 6. In this experiment, we drove Rabi **oscillations** ...**qubit** to a separate lumped-element superconducting readout resonator, ...**qubit** flux bias, with no averaging. See text for details. fig.phase...**qubits** can be read out simultaneously using frequency multiplexing on ...**oscillations** for **qubits** Q 1 - Q 4 respectively, with the **qubits** driven...**frequencies** for the **qubit** in the left and right wells, marked by the dashed...**oscillations** in panels (a)-(d) compared to the multiplexed readout in ...**frequency** for maximum visibility. (b) Reflected phase as a function of...**qubit** Josephson junction. Each **qubit** is coupled to its readout resonator...**qubits**. Using a quantum circuit with four phase **qubits**, we couple each...**qubits**, a significant advantage for scaling up to larger numbers of **qubits**...**frequency**-multiplexed readout. Multiplexed readout signals I p and Q p...**qubit**’s | g ↔ | e transition and read out the **qubit** states simultaneously...**qubit** was projected onto the | g or the | e state....**qubit** | g ↔ | e transition frequency of 6-7 GHz), with loaded resonance...**qubits** Q 1 to Q 4 . We then drove each **qubit** separately using an on-resonance...**qubit** projective measurement, where a current pulse allows a **qubit** in ...**frequency** shifts as large as ∼ 150 kHz for the **qubit** between the two wells...**frequency** (averaged 900 times), for the **qubit** in the left ( L , blue) ...**qubit** chip. Reflected signals pass back through the circulator, through...**frequency**-multiplexed readout scheme for superconducting phase **qubits**....**qubits**, we couple each **qubit** to a separate lumped-element superconducting...**oscillations** measured simultaneously for all the **qubits**, using the same...**frequency**, with the **qubit** prepared first in the left and then in the right...**qubits** ... We introduce a **frequency**-multiplexed readout scheme for superconducting phase **qubits**. Using a quantum circuit with four phase **qubits**, we couple each **qubit** to a separate lumped-element superconducting readout resonator, with the readout resonators connected in parallel to a single measurement line. The readout resonators and control electronics are designed so that all four **qubits** can be read out simultaneously using **frequency** multiplexing on the one measurement line. This technology provides a highly efficient and compact means for reading out multiple **qubits**, a significant advantage for scaling up to larger numbers of **qubits**.

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Contributors: Agarwal, S., Rafsanjani, S. M. Hashemi, Eberly, J. H.

Date: 2012-01-13

**qubit** case....**qubit** system is extended to the multi-**qubit** case. For a two-**qubit** system...single-**qubit** case where only one Rabi frequency determines the evolution...two-**qubit** analytic formula matches well to the corresponding numerical...**qubits** are quasi-degenerate, i.e., with **frequencies** much smaller than ...**qubits** are coupled to the **oscillator** so strongly, or are so far detuned...**oscillator**. For an **oscillator** of mass M and **frequency** ω the zero point...**oscillator** is allowed to be an appreciable fraction of the **oscillator** **frequency**. In this parameter regime, the dynamics of the system can neither...one-**qubit** and (b.) two-**qubit** probability dynamics, and (c.) shows that...**qubit**-**qubit** entanglement. Both number state and coherent state preparations...**frequencies** of the **qubits** are much smaller than the **oscillator** **frequency**...**qubit** interacting with a common **oscillator** mode is extended beyond the...two-**qubit** TC model derived within the RWA is valid. At resonance, the ...**qubits** are much smaller than the oscillator frequency and the coupling...two-**qubit** numerical evaluation, which comes from the ω - 2 ω beat note...**oscillator** **frequency**, ω 0 ≪ ω , while the coupling between the **qubits** ...**qubits** can be seen....two-**qubit** case. Qualitative differences between the single-**qubit** and the...two-**qubit** TC model beyond the validity regime of RWA. The regime of parameters...**qubit** interacting with a common oscillator mode is extended beyond the...**qubits**...**qubit**....**oscillator** state with the lowest of the S x states. Note the breakup in...two-**qubit** dynamics that are different from the single **qubit** case, including ... The Tavis-Cummings model for more than one **qubit** interacting with a common **oscillator** mode is extended beyond the rotating wave approximation (RWA). We explore the parameter regime in which the **frequencies** of the **qubits** are much smaller than the **oscillator** **frequency** and the coupling strength is allowed to be ultra-strong. The application of the adiabatic approximation, introduced by Irish, et al. (Phys. Rev. B \textbf{72}, 195410 (2005)), for a single **qubit** system is extended to the multi-**qubit** case. For a two-**qubit** system, we identify three-state manifolds of close-lying dressed energy levels and obtain results for the dynamics of intra-manifold transitions that are incompatible with results from the familiar regime of the RWA. We exhibit features of two-**qubit** dynamics that are different from the single **qubit** case, including calculations of **qubit**-**qubit** entanglement. Both number state and coherent state preparations are considered, and we derive analytical formulas that simplify the interpretation of numerical calculations. Expressions for individual collapse and revival signals of both population and entanglement are derived.

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Contributors: Vierheilig, Carmen, Bercioux, Dario, Grifoni, Milena

Date: 2010-10-22

**qubit** dynamics is investigated. In particular, an analytic formula for...**qubit**’s evolution described by q t . This can be achieved within an effective...**qubit**, an intermediate nonlinear oscillator and an Ohmic bath. linearbath...**qubit** plus **oscillator** system (yellow (light grey) box) and accounts afterwards...**qubit** dynamics. The comparison of linear versus nonlinear case is done...**qubit** coupled to a nonlinear quantum **oscillator**, the latter coupled to...**oscillator** (red (dark grey) box). In the harmonic approximation the effective...**oscillator**. To determine the actual form of the susceptibility, we consider...**qubit**, an intermediate nonlinear **oscillator** and an Ohmic bath. linearbath...**qubit**, -the system of interest-, coupled to a nonlinear quantum **oscillator**...**qubit**, -the system of interest-, coupled to a nonlinear quantum oscillator...**frequency**, as shown in Fig. CompLorentz....**oscillator** within linear response theory in the driving amplitude. Knowing...**qubit** dynamics: In the first approach one determines the eigenvalues and...**qubit** coupled to a nonlinear quantum oscillator, the latter coupled to...**frequencies** with respect to the linear case. As a consequence the relative...**qubit** state we couple the **qubit** linearly to the oscillator with the coupling...**oscillator** and the Ohmic bath are put together, as depicted in Figure ...**qubit** dynamics. This composed system can be mapped onto that of a **qubit**...**qubit**-nonlinear **oscillator** system....**qubit**-nonlinear oscillator system....**qubit**'s population difference is derived. Within the regime of validity...**qubit** plus oscillator system (yellow (light grey) box) and accounts afterwards...**qubit** coupled to a dissipative nonlinear quantum oscillator: an effective...**qubit** state we couple the **qubit** linearly to the **oscillator** with the coupling...**qubit** dynamics. ... We consider a **qubit** coupled to a nonlinear quantum **oscillator**, the latter coupled to an Ohmic bath, and investigate the **qubit** dynamics. This composed system can be mapped onto that of a **qubit** coupled to an effective bath. An approximate mapping procedure to determine the spectral density of the effective bath is given. Specifically, within a linear response approximation the effective spectral density is given by the knowledge of the linear susceptibility of the nonlinear quantum **oscillator**. To determine the actual form of the susceptibility, we consider its periodically driven counterpart, the problem of the quantum Duffing **oscillator** within linear response theory in the driving amplitude. Knowing the effective spectral density, the **qubit** dynamics is investigated. In particular, an analytic formula for the **qubit**'s population difference is derived. Within the regime of validity of our theory, a very good agreement is found with predictions obtained from a Bloch-Redfield master equation approach applied to the composite **qubit**-nonlinear **oscillator** system.

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Contributors: Hausinger, Johannes, Grifoni, Milena

Date: 2010-07-30

**oscillator** **frequency** approaches unity and goes beyond. In this regime ...**oscillator** **frequency** Ω , ε = l Ω . In this case we found that the levels...**qubit**-**oscillator** detuning. Furthermore, the dynamics is not governed anymore...**frequency** peaks coming from the two dressed **oscillation** **frequencies** Ω ...**Qubit**-oscillator system: An analytical treatment of the ultra-strong coupling...**qubit** for an **oscillator** at low temperature. We consider the coupling strength...**oscillations** **frequency** Ω j l . For l being not an integer those doublets...**qubit**-oscillator detuning. Furthermore, the dynamics is not governed anymore...**qubit** for an oscillator at low temperature. We consider the coupling strength...**qubit** ( ε / Ω = 0.5 ) at resonance with the oscillator Δ b = Ω in the ...**frequencies** through a variation of the coupling....**qubit** ( ε / Ω = 0.5 ) at resonance with the **oscillator** Δ b = Ω in the ...**frequency** range. The lowest **frequency** peaks originate from transitions...**qubit** tunneling matrix element $\Delta$ we are able to enlarge the regime...**oscillations**. With increasing time small differences between numerical...**oscillation** **frequency** Ω j 0 . Numerical calculations and VVP predict group...**oscillation** **frequencies** Ω j 1 and Ω j 2 influence the longtime dynamics...**qubit** ( ε / Ω = 0.5 ) being at resonance with the oscillator ( Δ b = Ω...**qubit** ( ε / Ω = 0.5 ) being at resonance with the **oscillator** ( Δ b = Ω ... We examine a two-level system coupled to a quantum **oscillator**, typically representing experiments in cavity and circuit quantum electrodynamics. We show how such a system can be treated analytically in the ultrastrong coupling limit, where the ratio $g/\Omega$ between coupling strength and **oscillator** **frequency** approaches unity and goes beyond. In this regime the Jaynes-Cummings model is known to fail, because counter-rotating terms have to be taken into account. By using Van Vleck perturbation theory to higher orders in the **qubit** tunneling matrix element $\Delta$ we are able to enlarge the regime of applicability of existing analytical treatments, including in particular also the finite bias case. We present a detailed discussion on the energy spectrum of the system and on the dynamics of the **qubit** for an **oscillator** at low temperature. We consider the coupling strength $g$ to all orders, and the validity of our approach is even enhanced in the ultrastrong coupling regime. Looking at the Fourier spectrum of the population difference, we find that many **frequencies** are contributing to the dynamics. They are gathered into groups whose spacing depends on the **qubit**-**oscillator** detuning. Furthermore, the dynamics is not governed anymore by a vacuum Rabi splitting which scales linearly with $g$, but by a non-trivial dressing of the tunneling matrix element, which can be used to suppress specific **frequencies** through a variation of the coupling.

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Contributors: Shahriar, M. S., Pradhan, Prabhakar

Date: 2002-12-19

**oscillation** from the plot in (a). (c) The time-dependence of the Rabi **frequency**. Inset: BSO as a function of the absolute phase of the field...**qubit** operations due to the Bloch-Siegert Oscillation...**frequency** is comparable to the Bohr **frequency** so that the rotating wave...low-**frequency** transitions. We present a scheme for observing this effect...**oscillation**. (b) The BSO **oscillation** (amplified scale) by itself, produced...**oscillation** is present with the Rabi **oscillation**. We discuss how the sensitivity...**Oscillation** (BSO): (a) The population of state | 1 , as a function of ... We show that if the Rabi **frequency** is comparable to the Bohr **frequency** so that the rotating wave approximation is inappropriate, an extra **oscillation** is present with the Rabi **oscillation**. We discuss how the sensitivity of the degree of excitation to the phase of the field may pose severe constraints on precise rotations of quantum bits involving low-**frequency** transitions. We present a scheme for observing this effect in an atomic beam.

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