Effect of relativistic motion on witnessing nonclassicality of quantum states

We show that the operational definition of nonclassicality of a quantum state depends on the motion of the observer. We use the relativistic Unruh-DeWitt detector model to witness nonclassicality of the probed field state. It turns out that the witness based on the properties of the $P$ representation of the quantum state depends on the trajectory of the detector. Inertial and noninertial motion of the device have qualitatively different impact on the performance of the witness.

Figure 1

Witness function $\left|W\right(t\left)\right|$ for the Fock state $|1\rangle$ and the Schrödinger cat state $|{\psi }_{\text{SC}}\left({\alpha }_0\right)\rangle$, and the following set of parameter values: $\lambda =1.7$, ${\omega }_{\text{ho}}=4/\sqrt{\pi }$, $m=1$, $L=2$, and ${\alpha }_0=1$.

Figure 2

Witness function $|W_{k_0}\left(\tau \right)|$ corresponding to the initial Fock state ${|\mathrm{\Psi }\rangle }_{k_0}={|0\rangle }_{k\ne k_0}\otimes {|1\rangle }_{k_0}$ for the detector moving with a constant velocity $v$ and the following set of parameters: $k_0=5000$, $L=10000$, $x_0=L/2k_0$, $\lambda =2\sqrt{k_0}$, and $m=1$.

Figure 3

Time-averaged $|W_{k_0}\left(\tau \right)|$ as a function of velocity $v$, with averaging time window $\tau \in \{0,500\}$ for the following parameter values: $k_0=5000$, $L=10000$, $x_0=L/2k_0$, $\lambda =2\sqrt{k_0}$, and $m=1$. The plot is shown in a logarithmic scale.

Figure 4

Witness function $|W_{k_0}\left(\tau \right)|$ corresponding to the initial Fock state ${|\mathrm{\Psi }\rangle }_{k_0}={|0\rangle }_{k\ne k_0}\otimes {|1\rangle }_{k_0}$ for the detector moving with a constant acceleration, and the following set of parameter values: $k_0=5000$, $L=10000$, $x_0=1$, $\lambda =2\sqrt{k_0}$, and $m=1$.

Figure 5

Witness function $|W_{k_0}\left(T\right)|$ corresponding to the initial Fock state ${|\mathrm{\Psi }\rangle }_{k_0}={|0\rangle }_{k\ne k_0}\otimes {|1\rangle }_{k_0}$, as a function of acceleration, evaluated at $T=500$ and for the following parameter values: $k_0=5000$, $L=10000$, and $m=1$.

Figure 6

Witness function $|W_{k_0}\left(\tau \right)|$ corresponding to the initial Schrödinger cat state ${|\mathrm{\Psi }\rangle }_{k_0}={|0\rangle }_{k\ne k_0}\otimes {|{\mathrm{\Psi }}_{\text{SC}}\left({\alpha }_0\right)\rangle }_{k_0}$ for the detector moving with a constant acceleration, and the following set of parameter values: $a=0.8$, $k=5000$, $L=10000$, $x_0=1$, $\lambda =2\sqrt{k_0}$, and $m=1$.

Figure 7

Witness function $|W_{k_0}\left(T\right)|$ corresponding to the initial Schrödinger cat state ${|\mathrm{\Psi }\rangle }_{k_0}={|0\rangle }_{k\ne k_0}\otimes {|{\mathrm{\Psi }}_{\text{SC}}\left({\alpha }_0\right)\rangle }_{k_0}$ as a function of ${\alpha }_0$, evaluated at $T=100$ and for the following parameter values: $a=0.8$, $k=5000$, $L=10000$, $x_0=1$, $\lambda =2\sqrt{k_0}$, and $m=1$.

Figure 8

Witness function $|W_{k_0}\left(T\right)|$ corresponding to the initial Schrödinger cat state ${|\mathrm{\Psi }\rangle }_{k_0}={|0\rangle }_{k\ne k_0}\otimes {|{\mathrm{\Psi }}_{\text{SC}}\left({\alpha }_0\right)\rangle }_{k_0}$ as a function of acceleration, evaluated at $T=1000$ and for the following parameter values: $k=5000$, $L=10000$, $x_0=1$, $\lambda =2\sqrt{k_0}$, and $m=1$.