  We subject a falling cloud of cold cesium atoms to periodic kicks from a
sinusoidal potential created by a vertical standing wave of off-resonant laser
light. By controllably accelerating the potential, we show quantum accelerator
mode dynamics to be highly sensitive to the effective gravitational
acceleration when this is close to specific, resonant values. This quantum
sensitivity to a control parameter is reminiscent of that associated with
classical chaos, and promises techniques for precision measurement.
