Magnetic flux in a mesoscopic SQUID controlled by nonclassical electromagnetic fields

We analyze SQUID coupled to a nonclassical electromagnetic field (NEM) and show that properties of the SQUID can be manipulated by a choice of a state of NEM. In particular, energy or fluctuations of magnetic flux threading the loop of the SQUID can be resolved into separate lines for each photon number state of one-mode NEM. The impact of two-mode NEM prepared in entangled Bell states is discussed. The findings suggest an experimental method of detection of photon states: the SQUID response is dependent on the number of photons in one-mode NEM and on the Bell states of a two-mode NEM.

Figure 1

(Color online) The potential $V\left(x\right)$ in the presence of number eigenstates. The curve labeled as $C$ in panel (b) represents the system in an empty space (’classical vacuum’). The “highlighted” potentials in panel (a) correspond to $N=0,1,2,12$.

Figure 2

(Color online) The second moment and the entropy of the magnetic flux in the SQUID irradiated by a nonclassical electromagnetic field in the number eigenstates. The initial state is assumed Gaussian, i.e., initially the distribution of the magnetic flux is such that $p\left(x,0\right)\sim N\left(0,0.1\right)$.

Figure 3

(Color online) The second moment and the entropy of the magnetic flux in the SQUID irradiated by a nonclassical two-mode electromagnetic field in the entangled number eigenstates. ${\omega }_1={\omega }_2=10$. The initial state $p\left(x,0\right)$ is the same as in Fig. 2.

Figure 4

(Color online) Stationary probability density of the magnetic flux in the SQUID in different vacuums: classical empty space, nonthermal $|0⟩$, and thermal Eq. (19). For thermal vacuum it is set $\hslash \omega /k_{B}T=1$.