Quantum Bits Manipulate Photon Propagation in Groundbreaking Study

The manipulation of photons in a one-dimensional waveguide coupled to an array of two-level atoms, or qubits, has significant implications for quantum devices and quantum information technologies. Researchers have extensively studied the transmission of single photons through arrays of qubits embedded in 1D open waveguides, but most calculations neglect the dynamics of the system. A new study aims to fill this gap by deriving a time-dependent dynamical theory for qubit amplitudes and transmitted and reflected spectra.

The study reveals that the requirement for photon-qubit coupling to exist only for positive frequencies can significantly change the dynamics of the system, leading to an additional dipole-dipole interaction between qubits. This interaction results in the violation of phase coherence between them, crucially affecting the spectral lines of transmitted and reflected photons.

Can Quantum Bits Be Used to Manipulate Photon Propagation?

The manipulation of photons in a one-dimensional waveguide coupled to an array of two-level atoms, or qubits, has significant implications for quantum devices and quantum information technologies. Quantum bits can be implemented using various quantum systems, such as trapped ions, photons, and quantum dots. In particular, superconducting qubits have emerged as a leading candidate for scalable quantum processor architecture.

The transmission of a single photon through an array of two-level atoms embedded in a 1D open waveguide has been extensively studied both theoretically and experimentally. Most theoretical calculations of the transmitted and reflected photon amplitudes in a 1D open waveguide with atoms placed inside have been performed within the framework of stationary theory in configuration space or alternative methods such as Lippmann-Schwinger scattering theory, input-output formalism, non-Hermitian Hamiltonian, and matrix methods.

However, these calculations often neglect the dynamics of the system, which can lead to a lack of understanding of the underlying physics. In this study, we aim to fill this gap by deriving a time-dependent dynamical theory for qubit amplitudes and transmitted and reflected spectra. This theory will allow us to investigate the dynamics of single-photon transport through a qubit chain coupled to a 1D nanophotonic waveguide.

The Importance of Dynamical Theory

The requirement for photon-qubit coupling to exist only for positive frequencies can significantly change the dynamics of the system. This requirement leads to an additional photon-mediated dipole-dipole interaction between qubits, resulting in the violation of phase coherence between them. Furthermore, the spectral lines of transmitted and reflected spectra crucially depend on the shape of the incident pulse and the initial distance between the pulse center and the first qubit in the chain.

To understand these dynamics, we need to develop a time-dependent dynamical theory that takes into account the interactions between the qubits and the photonic waveguide. This theory will allow us to investigate the behavior of single-photon transport through a qubit chain and its implications for quantum information technologies.

Theoretical Framework

Our theoretical framework is based on the Schrödinger equation, which describes the time evolution of the system. We assume that the qubits are coupled to the photonic waveguide through a dipole-dipole interaction, which is mediated by the photon field. This interaction leads to an additional term in the Hamiltonian, which represents the exchange of photons between the qubits.

To solve the Schrödinger equation, we use a combination of analytical and numerical methods. We first derive a set of coupled differential equations that describe the time evolution of the qubit amplitudes. These equations are then solved numerically using a finite-difference method.

Numerical Results

We apply our theoretical framework to one-qubit and two-qubit systems. For these cases, we obtain explicit expressions for the qubit amplitudes and the photon radiation spectra as time tends to infinity. We also calculate the line shapes of transmitted and reflected photons for an incident Gaussian wave packet.

Our numerical results show that the dynamics of single-photon transport through a qubit chain are significantly affected by the requirement for photon-qubit coupling to exist only for positive frequencies. This requirement leads to an additional dipole-dipole interaction between qubits, which results in the violation of phase coherence between them.

Conclusion

In conclusion, we have developed a time-dependent dynamical theory for single-photon transport through a qubit chain coupled to a 1D nanophotonic waveguide. Our theory takes into account the interactions between the qubits and the photonic waveguide, which are mediated by the photon field. We have applied our theoretical framework to one-qubit and two-qubit systems and obtained explicit expressions for the qubit amplitudes and the photon radiation spectra.

Our results show that the dynamics of single-photon transport through a qubit chain are significantly affected by the requirement for photon-qubit coupling to exist only for positive frequencies. This requirement leads to an additional dipole-dipole interaction between qubits, which results in the violation of phase coherence between them.

Future Directions

Our study provides a foundation for further research on the dynamics of single-photon transport through a qubit chain. Future studies could investigate the effects of different pulse shapes and initial distances between the pulse center and the first qubit in the chain. Additionally, our theory could be extended to include more complex systems, such as multiple qubits or non-linear interactions.