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Hermann Feshbach predicted fifty years ago that when two atomic nuclei are scattered within an open entrance channel-- the state observable at infinity, they may enter an intermediate closed channel -- the locally bounded state of the nuclei. If the energy of a bound state of in the closed channel is fine-tuned to match the relative kinetic energy, then the open channel and the closed channel resonate, so that the scattering length becomes divergent. We find that this so-called Feshbach resonance phenomenon not only exists during the collisions of massive particles, but also emerges during the coherent transport of massless particles, that is, photons confined in the coupled resonator arrays cite{lzhou08}. We implement the open and the closed channels inside a pair of such arrays, linked by a separated cavity or a tunable qubit. When a single photon is bounded inside the closed channel by setting the relevant physical parameters appropriately, the vanishing transmission appears to display this photonic Feshbach resonance. The general construction can be implemented through various experimentally feasible solid state systems, such as the couple defected cavities in photonic crystals. The numerical simulation based on finite-different time-domain(FDTD) method confirms our conceive about physical implementation.
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The projection-operator formalism of Feshbach is applied to resonance scattering in a single-channel case. The method is based on the division of the full function space into two segments, internal (localized) and external (infinitely extended). The spectroscopic information on the resonances is obtained from the non-Hermitian effective Hamilton operator $H_{rm eff}$ appearing in the internal part due to the coupling to the external part. As well known, additional so-called cut-off poles of the $S$-matrix appear, generally, due to the truncation of the potential. We study the question of spurious $S$ matrix poles in the framework of the Feshbach formalism. The numerical analysis is performed for exactly solvable potentials with a finite number of resonance states. These potentials represent a generalization of Bargmann-type potentials to accept resonance states. Our calculations demonstrate that the poles of the $S$ matrix obtained by using the Feshbach projection-operator formalism coincide with both the complex energies of the physical resonances and the cut-off poles of the $S$-matrix.
A new type of supersymmetric transformations of the coupled-channel radial Schroedinger equation is introduced, which do not conserve the vanishing behavior of solutions at the origin. Contrary to usual transformations, these ``non-conservative transformations allow, in the presence of thresholds, the construction of potentials with coupled scattering matrices from uncoupled potentials. As an example, an exactly-solvable potential matrix is obtained which provides a very simple model of Feshbach-resonance phenomenon.
We demonstrate a p$-wave optical Feshbach resonance (OFR) using purely long-range molecular states of a fermionic isotope of ytterbium ^{171}Yb, following the proposition made by K. Goyal et al. [Phys. Rev. A 82, 062704 (2010)]. The p-wave OFR is clearly observed as a modification of a photoassociation rate for atomic ensembles at about 5 micro-Kelvins. A scattering phase shift variation of delta eta=0.022 rad is observed with an atom loss rate coefficient K=28.0*10^{-12} cm^3/s.
We analyse the formation of ultracold 7Li133Cs molecules in the rovibrational ground state through photoassociation into the B1Pi state, which has recently been reported [J. Deiglmayr et al., Phys. Rev. Lett. 101, 133004 (2008)]. Absolute rate constants for photoassociation at large detunings from the atomic asymptote are determined and are found to be surprisingly large. The photoassociation process is modeled using a full coupled-channel calculation for the continuum state, taking all relevant hyperfine states into account. The enhancement of the photoassociation rate is found to be caused by an `echo of the triplet component in the singlet component of the scattering wave function at the inner turning point of the lowest triplet a3Sigma+ potential. This perturbation can be ascribed to the existence of a broad Feshbach resonance at low scattering energies. Our results elucidate the important role of couplings in the scattering wave function for the formation of deeply bound ground state molecules via photoassociation.
We theoretically investigate the control of a magnetic Feshbach resonance using a bound-to-bound molecular transition driven by spatially modulated laser light. Due to the spatially periodic coupling between the ground and excited molecular states, there exists a band structure of bound states, which can uniquely be characterized by some extra bumps in radio-frequency spectroscopy. With the increasing of coupling strength, the series of bound states will cross zero energy and directly result in a number of scattering resonances, whose position and width can be conveniently tuned by the coupling strength of the laser light and the applied magnetic field (i.e., the detuning of the ground molecular state). In the presence of the modulated laser light, universal two-body bound states near zero-energy threshold still exist. However, compared with the case without modulation, the regime for such universal states is usually small. An unified formula which embodies the influence of the modulated coupling on the resonance width is given. The spatially modulated coupling also implies a local spatially varying interaction between atoms. Our work proposes a practical way of optically controlling interatomic interactions with high spatial resolution and negligible atomic loss.
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