BEC and Optical Lattices
... by interfering laser beams and produce periodic trap potentials for the BEC atoms. The trap parameters defined by an optical lattice can be controlled in a very wide range by the laser parameters yielding a versatile trap geometry [16]. Optical lattices are ideally suited to produce and study one an ...
... by interfering laser beams and produce periodic trap potentials for the BEC atoms. The trap parameters defined by an optical lattice can be controlled in a very wide range by the laser parameters yielding a versatile trap geometry [16]. Optical lattices are ideally suited to produce and study one an ...
Quantum Expanders: Motivation and Constructions
... graph G = (V, E) into a corresponding quantum superoperator T . However, the analysis shows that the spectral gap of T is 0, and more specifically, T has |V | eigenspaces each of dimension |V |, with eigenvalues ~λ = (λ1 = 1, . . . , λ|V | ), where ~λ is the spectrum of the Cayley graph. Our first c ...
... graph G = (V, E) into a corresponding quantum superoperator T . However, the analysis shows that the spectral gap of T is 0, and more specifically, T has |V | eigenspaces each of dimension |V |, with eigenvalues ~λ = (λ1 = 1, . . . , λ|V | ), where ~λ is the spectrum of the Cayley graph. Our first c ...
Paired Hall states
... arbitrarily weak attractions. For this reason, the residual interactions may have a large effect even in the small-E regime where they are small and their effects are reliably calculable. In fact we shall soon argue that the residual interactions do trigger the pairing instability. They give us a p- ...
... arbitrarily weak attractions. For this reason, the residual interactions may have a large effect even in the small-E regime where they are small and their effects are reliably calculable. In fact we shall soon argue that the residual interactions do trigger the pairing instability. They give us a p- ...
Quantum Computer Compilers - Computer Science, Columbia
... The Future of Quantum Hardware • The future does not necessarily belong to the ion trappers: for example, electron spins in quantum dots, superconducting qubits, ultracold neutral atoms are all making impressive progress. • But ion traps have a head start, and some serious effort has been devoted t ...
... The Future of Quantum Hardware • The future does not necessarily belong to the ion trappers: for example, electron spins in quantum dots, superconducting qubits, ultracold neutral atoms are all making impressive progress. • But ion traps have a head start, and some serious effort has been devoted t ...
Department of Physics, Chemistry and Biology Master’s Thesis
... In order to explore a quantum version of a discrete nonlinear Schrödinger equation (DNLS), we quantize one nonlinear Schrödinger model, which is used to study different physical systems, e.g. coupled Bose-Einstein condensates. We will focus on small systems, like Dimer and Trimer. In our efforts to ...
... In order to explore a quantum version of a discrete nonlinear Schrödinger equation (DNLS), we quantize one nonlinear Schrödinger model, which is used to study different physical systems, e.g. coupled Bose-Einstein condensates. We will focus on small systems, like Dimer and Trimer. In our efforts to ...
Topological order at finite temperature?
... “A system is in a topological phase if, at low temperatures, energies, and wavelengths*, all observable properties (e.g. correlation functions) are invariant under smooth deformations (diffeomorphisms) of the spacetime manifold in which the system lives.” (i.e., all observable properties are indepen ...
... “A system is in a topological phase if, at low temperatures, energies, and wavelengths*, all observable properties (e.g. correlation functions) are invariant under smooth deformations (diffeomorphisms) of the spacetime manifold in which the system lives.” (i.e., all observable properties are indepen ...
Particle in a box
In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems. In classical systems, for example a ball trapped inside a large box, the particle can move at any speed within the box and it is no more likely to be found at one position than another. However, when the well becomes very narrow (on the scale of a few nanometers), quantum effects become important. The particle may only occupy certain positive energy levels. Likewise, it can never have zero energy, meaning that the particle can never ""sit still"". Additionally, it is more likely to be found at certain positions than at others, depending on its energy level. The particle may never be detected at certain positions, known as spatial nodes.The particle in a box model provides one of the very few problems in quantum mechanics which can be solved analytically, without approximations. This means that the observable properties of the particle (such as its energy and position) are related to the mass of the particle and the width of the well by simple mathematical expressions. Due to its simplicity, the model allows insight into quantum effects without the need for complicated mathematics. It is one of the first quantum mechanics problems taught in undergraduate physics courses, and it is commonly used as an approximation for more complicated quantum systems.