Controlling Qubit Relaxation in 1-3 Dimensions*

In the circuit QED architecture, the coupling of a qubit through its associated cavity to the cavity drive port sets the ultimate limit on coherence.  For lumped element realizations this so-called single-mode Purcell limit stringently limits qubit coherence, unless an external filter (often referred to as a Purcell filter) is used to suppress photon emission at the qubit's frequency.  However, in 2- and 3-D circuits, we can often greatly exceed the single mode Purcell limit [Houck, et.al, PRL (2008)].  In this talk, we present a method for visualizing transmon fields to find port placements which can achieve both large cavity bandwidths and long qubit lifetimes.  We find that when the qubit frequency is below the lowest cavity mode, this effect cannot be explained by interference between multiple cavity modes, but rather the variation of the qubit mode's fields in space.  We will present data from transmons in both 3-D post cavity and chip-in-tube geometries.  We have achieved coherences as high as 100 microseconds in systems with strong qubit-cavity couplings, short cavity lifetimes, and no external Purcell filtering.  This technique can also readily be extended to planar qubit/resonator designs and is thus broadly useful across many implementations of superconducting circuits.