  We establish $L^2$-exponential convergence rate for three popular piecewise
deterministic Markov processes for sampling: the randomized Hamiltonian Monte
Carlo method, the zigzag process, and the bouncy particle sampler. Our analysis
is based on a variational framework for hypocoercivity, which combines a
Poincar\'{e}-type inequality in time-augmented state space and a standard $L^2$
energy estimate. Our analysis provides explicit convergence rate estimates,
which are more quantitative than existing results.
