The phenomenon of coherent population trapping (CPT) of an atom (or solid state "artificial atom"), and the associated effect of electromagnetically induced transparency (EIT), are clear demonstrations of quantum interference due to coherence in multilevel quantum systems. We report observation of CPT in a superconducting phase qubit by simultaneously driving two coherent transitions in a Lambda-type configuration, utilizing the three lowest lying levels of a local minimum of a phase qubit. We observe 60(+/-7)% suppression of the excited state population under conditions of CPT resonance. We present data and matching theoretical simulations showing the development of CPT in time. Finally, we used the observed time dependence of the excited state population to characterize quantum dephasing times of the system.

We propose bulk duals for certain coarse-grained entropies of boundary regions. The 'one-point entropy' is defined in the conformal field theory by maximizing the entropy in a domain of dependence while fixing the one-point functions. We conjecture that this is dual to the area of the edge of the region causally accessible to the domain of dependence (i.e. the 'causal holographic information' of Hubeny and Rangamani). The 'future onepoint entropy' is defined by generalizing this conjecture to future domains of dependence and their corresponding bulk regions. We show that the future one-point entropy obeys a nontrivial second law. If our conjecture is true, this answers the question "What is the field theory dual of Hawking's area theorem?"

The averaged null energy conditions (ANEC) states that, along a complete null curve, the negative energy fluctuations of a quantum field must be balanced by positive energy fluctuations. We use the AdS/CFT correspondence to prove the ANEC for a class of strongly coupled conformal field theories in flat spacetime. A violation of the ANEC in the field theory would lead to acausal propagation of signals in the bulk.

We explore several extensions of the generalized entropy construction of Lewkowycz and Maldacena, including a formulation that does not rely on preserving replica symmetry in the bulk. We show that an appropriately general ansatz for the analytically continued replica metric gives us the flexibility needed to solve the gravitational field equations beyond general relativity. As an application of this observation we study Einstein-Gauss-Bonnet gravity with a small Gauss-Bonnet coupling and derive the condition that the holographic entanglement entropy must be evaluated on a surface which extremizes the Jacobson-Myers entropy. We find that in both general relativity and Einstein-Gauss-Bonnet gravity replica symmetry breaking terms are permitted by the field equations, suggesting that they do not generically vanish.Comment: 24 pages, 3 figures. v3: fixed some more typos, v2: fixed minor typo

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