We investigate coherence in one- and two-photon optical systems, both theoretically and experimentally. In the first case, we develop the density operator representing a single photon state subjected to a non-dissipative coupling between observed (polarization) and unobserved (frequency) degrees of freedom. We show that an implementation of ``bang-bang'' quantum control protects photon polarization information from certain types of decoherence. In the second case, we investigate the existence of a "decoherence-free" subspace of the Hilbert space of two-photon polarization states under the action of a similar coupling. The density operator representation is developed analytically and solutions are obtained numerically. NOTE: This manuscript is taken from the author's undergraduate thesis (A.B. Dartmouth College, June 2000, advised by Dr. Walter E. Lawrence), under the supervision of Dr. Paul G. Kwiat.
We investigate coherence in one- and two-photon optical systems, both theoretically and experimentally. In the first case, we develop the density operator representing a single photon state subjected to a non-dissipative coupling between observed (polarization) and unobserved (frequency) degrees of freedom. We show that an implementation of ``bang-bang'' quantum control protects photon polarization information from certain types of decoherence. In the second case, we investigate the existence of a "decoherence-free" subspace of the Hilbert space of two-photon polarization states under the action of a similar coupling. The density operator representation is developed analytically and solutions are obtained numerically. NOTE: This manuscript is taken from the author's undergraduate thesis (A.B. Dartmouth College, June 2000, advised by Dr. Walter E. Lawrence), under the supervision of Dr. Paul G. Kwiat.
In recent years the interest in the manipulation of quantum systems has furthered new strategies for maintaining their coherence, continuously threatened by unwanted and uncontrollable interactions with the environment. Photons interact weakly with the surroundings. Even so decoherence may significantly affect their polarization state during the propagation within dispersive media because of the unavoidable presence of more than a single frequency in the envelope of the photon pulse. Here we report on a suppression of the polarization decoherence in a ring cavity obtained by properly retooling for the photon qubit the "bang-bang" protection technique already employed for nuclear spins and nuclear-quadrupole qubits. Our results show that bang-bang control can be profitably extended to all quantum information processes involving flying polarization qubits.
We explore the concepts of coherence and entanglement as they apply to both the classical and quantum natures of light. In the classical domain, we take inspiration from the tools and concepts developed in foundational quantum mechanics and quantum information science to gain a better understanding of classical coherence theory of light with multiple degrees of freedom (DoFs). First, we use polarization and spatial parity DoFs to demonstrate the notion of classical entanglement, and show that Bell's measure can serve as a useful tool in distinguishing between classical optical coherence theory. Second, we establish a methodical yet versatile approach called 'optical coherency matrix tomography' for reconstructing the coherency matrix of an electromagnetic beam with multiple DoFs. This technique exploits the analogy between this problem in classical optics and that of tomographically reconstructing the density matrix associated with multipartite quantum states in quantum information science. Third, we report the first experimental measurements of the 4 x 4 coherency matrix associated with an electromagnetic beam in which polarization and a spatial DoF are relevant, ranging from the traditional two-point Young's double slit to spatial parity and orbital angular momentum modes. In the quantum domain, we use the modal structure of classical fields to develop qubits and structure Hilbert spaces for use in quantum information processing. Advancing to three-qubit logic gates is an important step towards the success of optical schemes for quantum computing. We experimentally implement a variety of two- and three- qubit, linear and deterministic, single-photon, controlled, quantum logic gates using polarization and spatial parity qubits. Lastly, we demonstrate the implementation of two-qubit single-photon logic using polarization and orbital angular momentum qubits.
In the propagation of optical pulses through dispersive media, the frequency degree of freedom acts as an effective decohering environment on the polarization state of the pulse. Here we discuss the application of open-loop dynamical-decoupling techniques for suppressing such a polarization decoherence in one-way communication channels. We describe in detail the experimental proof of principle of the ``bang-bang'' protection technique recently applied to flying qubits in Damodarakurup et al. [Phys. Rev. Lett. 103, 040502 (2009)]. Bang-bang operations are implemented through appropriately oriented wave plates and dynamical decoupling is shown to be potentially useful to contrast a generic decoherence acting on polarization qubits propagating in dispersive media like optical fibers.
Decoherence may significantly affect the polarization state of optical pulses propagating in dispersive media because of the unavoidable presence of more than a single frequency in the envelope of the pulse. Here we report on the suppression of polarization decoherence in a ring cavity obtained by properly retooling for photonic qubits the "bang-bang" protection technique already employed for nuclear spins and nuclear-quadrupole qubits. Our results show that bang-bang control can be profitably extended to quantum information processes involving flying polarization qubits.
Quantum optics, the study of light at the level of its building blocks, \nhas been one of the frontiers of science. The arena of quantum optics \nhas been fruitful for investigations of a wide range of interesting questions, \nfrom those on the fundamental structures in driven dissipative \nsystems to those on applications of quantum information processing \nand quantum communication. \nThe first part of this thesis is concerned with one of the holy grails \nof quantum optics: an efficient transfer of energy (coupling) between \nsingle photons and matter degrees of freedom. From a certain point \nof view, the problem of efficient coupling is purely geometrical. The \nefficiency of coupling between an atom and light is difficult because \nit is difficult to shape the wavefunction of a single photon such \nthat it overlaps perfectly with the matter degree of freedom (emitter). \nThe first contribution of this thesis is addressing this issue by considering \nan emitter which perfectly matches the single photon plane-wave. \nMoreover, luckily, such an emitter is already realized in nature in the \nform of a two-dimensional crystal. We show that a new generation \nof two-dimensional semiconductors, transition metal dichalcogenide \n(TMD) monolayers, have especially favorable characteristics for allowing \nhighly efficient coupling between photons and matter degrees \nof freedom. \nOne of the most important goals in realizing an efficient coupling \nbetween photons and matter degrees of freedom is that unlike photons, \nmatter excitations interact with each other. Hence, if we would \nlike to have photons which act as if they interact, one possible way \nis to first convert them into matter excitations, and then transfer the \ncorrelations due matter interactions back to photons. As the second \ncontribution of this thesis, we demonstrate that TMD monolayers placed \nwithin a cavity can help us create photons which avoid each other \nas if they interact. The effect can be simply understood as the TMD \nmonolayer acting as a filter for photons, such that it only allows the \npassage of one photon at a time. \nBesides being the fundamental building block of light, photons also \nserve as mediators of interactions between charged particles. In a \nsense, two positive charges repel each other because there is always \na photon which lets them know that they are close to one another. \nOn the other hand, systems of many interacting particles behave in \na completely different way then when they are alone. It may even be \nargued that all physical phenomena at some level emerge from the \nbehavior of many interacting constituents. Given this point of view, \nit is crucial to find ways to control photons in order to control the \ninteractions that they mediate between matter degrees of freedom. \nAs the third contribution of this thesis, we analyze an experimental \nscheme where the control of photonic degrees of freedom can allow \nan experimentalist to modify the strength and range of interactions \nbetween matter. In particular, we propose squeezed photon states as \na resource to control such interactions. \nThe second part of this thesis is concerned with the emergent phenomena \narising in a system of many interacting particles. In particular, \nthe fourth contribution of this thesis considers the combination \nof two fascinating phenomena which emerges such condensed matter \nsystems: superconductivity and geometric effects in lattice band \nstructures. Separately, both superconductivity and the non-trivial geometrical \neffects in lattice systems are well-established subfields of condensed \nmatter physics. Yet only more recently, the combination of \nthese two phenomena were investigated in the context of topological \nsuperconductors, as well as other superconducting states which emerge \non top of band structures with non-trivial geometry. In our study, \nwe attempt at clarifying one of the ways that the non-trivial geometry \nassociated with the lattice band structure may affect the dynamics of \nan emergent superconducting state. Surprisingly, our analysis shows \nthat one of the most robust characteristics of the superconductor, vortices \nenclosing a quantum of magnetic flux, can be modified due to \ngeometrical effects.
The orbital angular momentum of photons, being defined in an infinite-dimensional discrete Hilbert space, offers a promising resource for high-dimensional quantum information protocols in quantum optics. The biggest obstacle to its wider use is presently represented by the limited set of tools available for its control and manipulation. Here, we introduce and test experimentally a series of simple optical schemes for the coherent transfer of quantum information from the polarization to the orbital angular momentum of single photons and vice versa. All our schemes exploit a newly developed optical device, the so-called "q-plate", which enables the manipulation of the photon orbital angular momentum driven by the polarization degree of freedom. By stacking several q-plates in a suitable sequence, one can also have access to higher-order angular momentum subspaces. In particular, we demonstrate the control of the orbital angular momentum m degree of freedom within the subspaces of |m| = 2h and |m| = 4h per photon.