Talitha Weiss

Accuracy of the capillary approximation for gas-filled kagomé-style photonic crystal fibers.

Precise knowledge of the group velocity dispersion in gas-filled hollow-core photonic crystal fiber is essential for accurate modeling of ultrafast nonlinear dynamics. Here we study the validity of the capillary approximation commonly used to calculate the modal refractive index in kagomé-style photonic crystal fibers. For area-preserving core radius a(AP) and core wall thickness t, measurements and finite element simulations show that the approximation has an error greater than 15% for wavelengths longer than 0.56√(a(AP)t), independently of the gas-filling pressure. By introducing an empirical wavelength-dependent core radius, the range of validity of the capillary approximation is extended out to a wavelength of at least 0.98√(a(AP)t).

Damage-free single-mode transmission of deep-UV light in hollow-core PCF.

Transmission of UV light with high beam quality and pointing stability is desirable for many experiments in atomic, molecular and optical physics. In particular, laser cooling and coherent manipulation of trapped ions with transitions in the UV require stable, single-mode light delivery. Transmitting even ~2 mW CW light at 280 nm through silica solid-core fibers has previously been found to cause transmission degradation after just a few hours due to optical damage. We show that photonic crystal fiber of the kagomé type can be used for effectively single-mode transmission with acceptable loss and bending sensitivity. No transmission degradation was observed even after >100 hours of operation with 15 mW CW input power. In addition it is shown that implementation of the fiber in a trapped ion experiment increases the coherence time of the internal state transfer due to an increase in beam pointing stability.

Topological Zeeman effect and circular birefringence in twisted photonic crystal fibers

The propagation of light guided in optical fibers is affected in different ways by bending or twisting. Here we treat the polarization properties of twisted six-fold symmetric photonic crystal fibers. Using a coordinate frame that follows the twisting structure, we show that the governing equation for the fiber modes resembles the Pauli equation for electrons in weak magnetic fields. This implies index splitting between left and right circularly polarized modes, which are degenerate in the untwisted fiber. We develop a theoretical model, based on perturbation theory and symmetry properties, to predict the observable circular birefringence (i.e., optical activity) associated with this splitting. Our overall conclusion is that optical activity requires the rotational symmetry to be broken so as to allow coupling between different total angular momentum states.

Quantum limit of laser cooling in dispersively and dissipatively coupled optomechanical systems

Mechanical oscillators can be cooled by coupling them to an optical or microwave cavity. Going beyond the standard quantum noise approach, we find an analytic expression for the steady-state phonon number in systems where the position of the mechanical oscillator modulates the cavity frequency as well as the cavity linewidth. We trace the origin for the quantum limit of cooling to fluctuations in the optical force both at and away from the mechanical frequency. Finally, we calculate the minimal phonon number for the different types of couplings. Our study elucidates how to beneficially combine dispersive and dissipative optomechanical couplings.

Strong-coupling effects in dissipatively coupled optomechanical systems

In this paper, we study cavity optomechanical systems in which the position of a mechanical oscillator modulates both the resonance frequency (dispersive coupling) and the linewidth (dissipative coupling) of a cavity mode. Using a quantum noise approach, we calculate the optical damping and the optically induced frequency shift. We find that dissipatively coupled systems feature two parameter regions providing amplification and two parameter regions providing cooling. To investigate the strong-coupling regime, we solve the linearized equations of motion exactly and calculate the mechanical and optical spectra. In addition to signatures of normal-mode splitting that are similar to the case of purely dispersive coupling, the spectra contain a striking feature that we trace back to the Fano line shape of the force spectrum. Finally, we show that purely dissipative coupling can lead to optomechanically induced transparency which will provide an experimentally convenient way of observing normal-mode splitting.

Quantum-coherent phase oscillations in synchronization

Recently, several studies have investigated synchronization in quantum-mechanical limit-cycle oscillators. However, the quantum nature of these systems remained partially hidden, since the dynamics of the oscillators phase was overdamped and therefore incoherent. We show that there exist regimes of underdamped and even quantum-coherent phase motion, opening up new possibilities to study quantum synchronization dynamics. To this end, we investigate the Van der Pol oscillator (a paradigm for a self-oscillating system) synchronized to an external drive. We derive an effective quantum model which fully describes the regime of underdamped phase motion and additionally allows us to identify the quality of quantum coherence. Finally, we identify quantum limit cycles of the phase itself.

General Linearized Theory of Quantum Fluctuations around Arbitrary Limit Cycles

The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its accuracy far from critical points or situations where the nonlinearity reaches the strong coupling regime, has turned it into a widespread technique, being the first method of choice in most works on the subject. However, such a technique finds strong practical and conceptual complications when one tries to apply it to situations in which the classical long-time solution is time dependent, a most prominent example being spontaneous limit-cycle formation. Here, we introduce a linearization scheme adapted to such situations, using the driven Van der Pol oscillator as a test bed for the method, which allows us to compare it with full numerical simulations. On a conceptual level, the scheme relies on the connection between the emergence of limit cycles and the spontaneous breaking of the symmetry under temporal translations. On the practical side, the method keeps the simplicity and linear scaling with the size of the problem (number of modes) characteristic of standard linearization, making it applicable to large (many-body) systems.

Theory of optical activity in twisted photonic crystal fibers

In optically active materials and devices, the plane of vibration of linearly polarized light is rotated due to different phase indices of left- and right-circularly (LC and RC) polarized light, i.e., there is circular birefringence. Optical fibers with high circular birefringence are able to maintain circular polarization states against external perturbations such as bending and mechanical stress. In this paper, we present theoretical and experimental analysis of optical activity in twisted photonic crystal fibers (PCFs).

Optical Activity Enhanced by Orbital Angular Momentum Resonances in Helically Twisted PCF

We demonstrate that twisted solid-core PCF develops strongly enhanced optical activity and circular dichroism in the vicinity of orbital angular momentum resonances in the cladding. It may be used as a circular polarizer.