George C. Cardoso

Precision Rotation Sensing and Interferometry Using Slow Lght

We show how a combination of pulsed and CW excitation enhance the sensitivity of a Mach-Zehnder interferometer and a Sagnac rotation sensor by the group index, which can be as high as ten million

In situ detection of the temporal and initial phase of the second harmonic of a microwave field via incoherent fluorescence

Measuring the amplitude and the absolute phase of a monochromatic microwave field at a specific point of space and time has many potential applications, including precise qubit rotations and wavelength quantum teleportation. Here we show how such a measurement can indeed be made using resonant atomic probes, via detection of incoherent fluorescence induced by a laser beam. This measurement is possible due to self-interference effects between the positive and negative frequency components of the field. In effect, the small cluster of atoms here act as a highly localized pick-up coil, and the fluorescence channel acts as a transmission line. 03.67.Hk, 03.67.Lx, 32.80.Qk Typeset using REVTEX 1 Measurement of the amplitude and the absolute phase of a monochromatic wave is challenging because in the most general condition the spatial distribution of the field around a point is arbitrary. Therefore, one must know the impedance of the system between the point of interest and the detector, and ensure that there is no interference with the ambient field. It is recently shown in the literature that the absolute phase measurement can be used for accurate qubit rotations [1-3] and quantum wavelength teleportation [4-6]. Before we describe the physics behind this process, it is instructive to define precisely what we mean by the term “absolute phase.” Consider, for example, a microwave field such that the magnetic field at a position R is given by B(t) = B0cos(ωt+φ)x̂, where ω is the frequency of the field, and φ is determined simply by our choice of the origin of time. The absolute phase is the sum of the temporal and the initial phase, i.e., ωt+φ. In order to illustrate how this phase can be observed directly, consider a situation where a cluster of non-interacting atoms are at rest at the same location. For simplicity, we assume each atom to be an ideal two-level system where a ground state |0> is coupled to an excited state |1> by this field B(t), with the atom initially in state |0>. The Hamiltonian for this interaction is: Ĥ = ε(σ0 − σz)/2 + g(t)σx, (1) where g(t) = −gocos(ωt+φ), gois the Rabi frequency, σi are the Pauli matrices, and the driving frequency ω = ε corresponds to resonant excitation. We consider g0 to be of the form g0(t) = g0M [1 − exp(−t/τsw)] with a switching time τsw relatively slow compared to other time scales in the system, i.e. τsw >> ω −1 and g 0M . As we have shown before [2,3], without the rotating wave approximation (RWA) and to the lowest order in η ≡(g0/4ω), the amplitudes of |0> and |1> at any time t are as follows : C0(t) = cos(g ′ 0(t)t/2) − 2ηΣ · sin(g ′ 0(t)t/2), (2) C1(t) = ie −i(ω [sin(g 0(t)t/2) + 2ηBΣ ∗ · cos(g′ 0(t)t/2)], (3)

Suppression of error in qubit rotations due to Bloch–Siegert oscillation via the use of off-resonant Raman excitation

The rotation of a quantum bit (qubit) is an important step in quantum computation. The rotation is generally performed using a Rabi oscillation. In a direct two-level qubit system, if the Rabi frequency is comparable to its resonance frequency, the rotating wave approximation is not valid, and the Rabi oscillation is accompanied by the so-called Bloch–Siegert oscillation (BSO) that occurs at twice the frequency of the driving field. One implication of the BSO is that for a given interaction time and Rabi frequency, the degree of rotation experienced by the qubit depends explicitly on the initial phase of the driving field. If this effect is not controlled, it leads to an apparent fluctuation in the rotation of the qubit. Here we show that when an off-resonant lambda system is used to realize a two-level qubit, the BSO is inherently negligible, thus eliminating this source of potential error.

Absence of Bloch-Siegert shift and oscillation in optically excited microwave transitions

We show that even when the effective Rabi frequency is large compared to the transition frequency, a microwave transition excited by an optically off-resonant Raman transition is immune to Bloch-Siegert effect and oscillation.