Yes, according to quantum field theory (QFT), there is a non-zero probability for a physical entity, such as a particle or a quantum field excitation, to quantum tunnel through a potential barrier even if the energy on the far side of the barrier is higher. This phenomenon is a consequence of the probabilistic nature of quantum mechanics.
In quantum mechanics, particles can exhibit wave-like behavior and can exist in superposition states, where they can be simultaneously on both sides of a potential barrier. The wavefunction of the particle represents the probability amplitude distribution, and the absolute value squared of the wavefunction gives the probability density of finding the particle at a particular location.
When a particle encounters a potential barrier, such as a step or a wall, classically, the particle would be entirely reflected if its energy is lower than the barrier height. However, in quantum mechanics, there is a finite probability for the particle to tunnel through the barrier and appear on the other side, even if its energy is lower than the barrier height.
This quantum tunneling effect arises because of the wave-particle duality in quantum mechanics. The wave nature of the particle allows it to penetrate the classically forbidden region of the barrier by spreading out and interfering with itself. As a result, there is a non-zero probability of finding the particle beyond the barrier, even if its energy is insufficient to surmount the barrier according to classical physics.
Quantum tunneling has been observed and plays a crucial role in various phenomena, such as radioactive decay, scanning tunneling microscopy, and tunneling in solid-state devices. It is a fundamental aspect of quantum mechanics that allows particles to exhibit behaviors that are not possible in classical physics.