Synthetic clock transitions via continuous dynamical decoupling

Decoherence of quantum systems due to uncontrolled fluctuations of the environment presents fundamental obstacles in quantum science. `Clock' transitions which are insensitive to such fluctuations are used to improve coherence, however, they are not present in all systems or for arbitrary system parameters. Here, we create a trio of synthetic clock transitions using continuous dynamical decoupling in a spin-1 Bose-Einstein condensate in which we observe a reduction of sensitivity to magnetic field noise of up to four orders of magnitude; this work complements the parallel work by Anderson et al. (submitted, 2017). In addition, using a concatenated scheme, we demonstrate suppression of sensitivity to fluctuations in our control fields. These field-insensitive states represent an ideal foundation for the next generation of cold atom experiments focused on fragile many-body phases relevant to quantum magnetism, artificial gauge fields, and topological matter.Comment: 8 pages, 4 figures, Supplemental material

Perpetual emulation threshold of PT-symmetric Hamiltonians

We describe a technique to emulate a two-level \PT-symmetric spin Hamiltonian, replete with gain and loss, using only the unitary dynamics of a larger quantum system. This we achieve by embedding the two-level system in question in a subspace of a four-level Hamiltonian. Using an \textit{amplitude recycling} scheme that couples the levels exterior to the \PT-symmetric subspace, we show that it is possible to emulate the desired behaviour of the \PT-symmetric Hamiltonian without depleting the exterior, reservoir levels. We are thus able to extend the emulation time indefinitely, despite the non-unitary \PT dynamics. We propose a realistic experimental implementation using dynamically decoupled magnetic sublevels of ultracold atoms.Comment: 15 pages, 8 figure

Fourier transform spectroscopy of a spin-orbit coupled Bose gas

We describe a Fourier transform spectroscopy technique for directly measuring band structures, and apply it to a spin-1 spin-orbit coupled Bose-Einstein condensate. In our technique, we suddenly change the Hamiltonian of the system by adding a spin-orbit coupling interaction and measure populations in different spin states during the subsequent unitary evolution. We then reconstruct the spin and momentum resolved spectrum from the peak frequencies of the Fourier transformed populations. In addition, by periodically modulating the Hamiltonian, we tune the spin-orbit coupling strength and use our spectroscopy technique to probe the resulting dispersion relation. The frequency resolution of our method is limited only by the coherent evolution timescale of the Hamiltonian and can otherwise be applied to any system, for example, to measure the band structure of atoms in optical lattice potentials

A Bose-Einstein Condensate in a Uniform Light-induced Vector Potential

We use a two-photon dressing field to create an effective vector gauge potential for Bose-condensed Rb atoms in the F=1 hyperfine ground state. The dressed states in this Raman field are spin and momentum superpositions, and we adiabatically load the atoms into the lowest energy dressed state. The effective Hamiltonian of these neutral atoms is like that of charged particles in a uniform magnetic vector potential, whose magnitude is set by the strength and detuning of Raman coupling. The spin and momentum decomposition of the dressed states reveals the strength of the effective vector potential, and our measurements agree quantitatively with a simple single-particle model. While the uniform effective vector potential described here corresponds to zero magnetic field, our technique can be extended to non-uniform vector potentials, giving non-zero effective magnetic fields.Comment: 5 pages, submitted to Physical Review Letter

Smooth analysis of the condition number and the least singular value

Let \a be a complex random variable with mean zero and bounded variance. Let $N_{n}$ be the random matrix of size $n$ whose entries are iid copies of \a and $M$ be a fixed matrix of the same size. The goal of this paper is to give a general estimate for the condition number and least singular value of the matrix $M + N_{n}$, generalizing an earlier result of Spielman and Teng for the case when \a is gaussian. Our investigation reveals an interesting fact that the "core" matrix $M$ does play a role on tail bounds for the least singular value of $M+N_{n}$. This does not occur in Spielman-Teng studies when \a is gaussian. Consequently, our general estimate involves the norm $\|M\|$. In the special case when $\|M\|$ is relatively small, this estimate is nearly optimal and extends or refines existing results.Comment: 20 pages. An erratum to the published version has been adde