Observation of the geometric amplitude factor in an optical system

Bouwmeester, D.; Karman, G. P.; Dekker, N. H.; Schrama, C. A.; Woerdman, J. P.

doi:10.1080/095003496154725

Cited by 3 publications

(5 citation statements)

References 17 publications

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“…It has already been suggested that, for example, the Yb atom could be used in conjunction with frequency modulated light [14,20], and it may also prove possible to manipulate the discrete optical levels in a resonator to show the same phenomena [21]. The transformation…”

Section: Discussionmentioning

confidence: 99%

“…These results can be derived in a similar manner as Eqs. (20), (21), (26), and (27). Thus, the excited-state populations at the crossings lie on just one sinusoid for cosine modulation and on another sinusoid for sine modulation.…”

Section: Excited-state Population At the Nodesmentioning

confidence: 99%

“…The parameter p can be found by deriving the transition probability from a given antinode to the next antinode, which, according to Eq. (21) with N = 0, is equal to 4p(1 − p); we choose to do this in the interval [−π/2, π/2] with sine modulation, ∆(t) = A sin ωt. Then, the parameter P can be found from the transition probability from a given lower (or upper) antinode to the next lower (or upper) antinode, which is equal to 4P (1 − 2p) 2 , according to Eq.…”

Section: Landau-zener Modelmentioning

confidence: 99%

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Population dynamics and phase effects in periodic level crossings

Garraway

Vitanov

1997

Phys. Rev. A

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We present an analytic study of the population dynamics of a two-state system interacting with an external field and subjected to periodic level crossings. We apply an evolution matrix approach to calculate the excited-state population at the crossings (the nodes) and at the antinodes. The results are expressed in terms of only two parameters: the transition probability p for a quarter period from a crossing to an antinode, and the transition probability P for a half period between two successive crossings. We find that the values of the excited-state population at the antinodes can form global (gross) structures. We show that these structures and the population dynamics as a whole are very sensitive to the initial phase ϕ of the frequency-modulated field, particularly in the limits ϕ = 0 (cosine modulation) and ϕ = π/2 (sine modulation). We calculate the parameters p and P by using two analytic approaches: one based on the original Landau-Zener model, and the other based on the finite Landau-Zener model. Both approaches unexpectedly lead to the same results. The notion of the global structures and the relevant parametrization in terms of p and P allow us to find various distinctive cases of population dynamics, such as population swapping, completely periodic

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Section: Discussionmentioning

confidence: 99%

Section: Excited-state Population At the Nodesmentioning

confidence: 99%

Section: Landau-zener Modelmentioning

confidence: 99%

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Population dynamics and phase effects in periodic level crossings

Garraway

Vitanov

1997

Phys. Rev. A

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“…Resembling behavior is known in vibrational mechanical modes [6]. In optics, anticrossings (also referred to as avoided crossings) with a gap in the transmission frequency have been reported in liquid-crystal etalons [7] and used to observe the geometric amplitude factor [8]. Crossing of optical resonances was recently reported [9] in spherical cavities.…”

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confidence: 99%

Static Envelope Patterns in Composite Resonances Generated by Level Crossing in Optical Toroidal Microcavities

et al. 2008

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We study level crossing in the optical whispering-gallery (WG) modes by using toroidal microcavities. Experimentally, we image the stationary envelope patterns of the composite optical modes that arise when WG modes of different wavelengths coincide in frequency. Numerically, we calculate crossings of levels that correspond with the observed degenerate modes, where our method takes into account the not perfectly transverse nature of their field polarizations. In addition, we analyze anticrossing with a large avoidance gap between modes of the same azimuthal number. Here we show experimentally and theoretically that optical resonances with a different number of wavelengths along the circumference can be tuned to cross in frequency. Modes of the same number of wavelengths, on the other hand, are shown to anticross with a large gap. Overall, diverse azimuthal and radial mode shapes are imaged, and modes with complex transverse shapes and polarizations are calculated. Using a fluorescent mode-mapping technique enabled imaging of noncircular mode patterns that signals crossing. This visual indication was hidden when we were using bare nonfluorescent cavities.Near the degeneracy region, modes exhibiting a different number of circumferential wavelengths are simultaneously excited with a single-frequency laser source to produce a standing interference envelope. Here, only modes circulating in one direction are examined. Level crossing of countercirculating modes is possible [10] but, in distinction to the relatively large spatial ''beats'' observed here, manifests itself as a fine standing-wave interference pattern with nodes lying just half an optical wavelength apart. Moreover, in experiments, countercirculating modes (of similar indices) are typically split (i.e., nondegenerate) [11][12][13] due to imperfect isotropy (broken axial symmetry). In our system, this split (10 7 Hz) is much smaller than the free spectral range (10 12 Hz); such a splitting and the type of anisotropy it originates from might therefore play only a minor role here in bringing levels close enough to cross.Optical resonators in general [14 -16] and dielectric whispering-gallery (WG) cavities [17,18] in particular have a set of discrete optical eigenfrequencies. For a geometry in which the wave equation is separable, such as a cylindrical or spherical resonator, each mode can be labeled by three integer indices. Normally, by convention, the resonance frequency increases monotonically with each mode index. In a dielectric ring, for example, a whispering-gallery mode with a fixed and small transverse mode index and a large azimuthal mode index of m 105, say, will have 105 wavelengths along the circumference and will resonate at an optical frequency higher than that of

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“…Alternatively, a geometrical phase can be generated by continuously varying the parameters θ and φ in a cyclic fashion [38,39]. Starting from θ = 0 one can perform a cyclic adiabatic evolution on the (θ, φ) plane along a loop C. As predicted by Equations (19)- (22), the qubit state |11 then acquires the geometrical phase…”

Section: B Stirap-based Geometrical Phase Gatementioning

confidence: 99%

Decoherence-free dynamical and geometrical entangling phase gates

Pachos

Beige

2004

Phys. Rev. A

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It is shown that entangling two-qubit phase gates for quantum computation with atoms inside a resonant optical cavity can be generated via common laser addressing, essentially, within one step. The obtained dynamical or geometrical phases are produced by an evolution that is robust against dissipation in form of spontaneous emission from the atoms and the cavity and demonstrates resilience against fluctuations of control parameters. This is achieved by using the setup introduced by Pachos and Walther [Phys. Rev. Lett. 89, 187903 (2002)] and employing entangling Raman-or STIRAP-like transitions that restrict the time evolution of the system onto stable ground states.03.67. Pp, 42.50.Pq

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Observation of the geometric amplitude factor in an optical system

Cited by 3 publications

References 17 publications

Population dynamics and phase effects in periodic level crossings

Population dynamics and phase effects in periodic level crossings

Static Envelope Patterns in Composite Resonances Generated by Level Crossing in Optical Toroidal Microcavities

Decoherence-free dynamical and geometrical entangling phase gates

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