[2020] [paper notes] Based on Rydberg atom——

Preface

type
$Terahertz+The\; antenna$
Periodical
$Journal\; of\; Physics$
author
$Chen\; Zhiwen,Yu\; Zhenyue,Liao\; Kaiyu,Huang\; Wei,Yan\; Hui,Zhu\; Shiliang$
Time
$2020$

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Rydberg principle

Rydberg Atom means The main quantum number $n>10$ Highly excited atom of

Rydberg The electric dipole moment of the atom is relatively low and the excited state is large 2 or 3 An order of magnitude
$$RydbergElectric\; dipole\; moment\propto n^2$$

So for microwave 、THz The electric field of wave has extremely high sensitivity
（ It can detect weak electric field signals ）

Rydberg atom Strong coupling with electric field , bring Rydberg Electromagnetically induced transparency effect involving energy levels （EIT effect ） The transparent peak of AT split , The distance between the two peaks after splitting is proportional to the Rabi frequency of the coupling

Electromagnetically induced transparency effect （EIT effect ）：
Be able to use Plus coherent light field To induce the atomic system Cancellation interference To counteract the absorption of certain light by the medium , Make opaque materials transparent

AT split ：
Involving multiple electronic states and their interactions , It is a high-order nonlinear phenomenon of the interaction between intense laser and matter ？

Rabi frequency ：
For a two-level system , We apply an electromagnetic wave , When the electromagnetic wave frequency is appropriate , The atoms in the system will continue E1 Energy levels and E2 Transition between energy levels , This phenomenon is called Rabi oscillation

Thus, the intensity measurement is transformed into frequency measurement by using quantum interference effect , Realize traceable and highly sensitive measurement of electromagnetic wave electric field intensity

$$Intensity\; measurement\stackrel{\text{Quantum interference effect}}{*}frequency\; measurement$$

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2012 Shaffer Group experiments

Coupling two through microwave field Rydberg The energy levels , utilize Rydberg Atomic EIT effect , And microwave AT split , Realize the precise measurement of microwave electric field intensity

$sensitivity\approx 30\mu V\cdot c{m}^{-1}\cdot H{z}^{-1/2}$
$E_{min}\approx 8\mu V/cm$

The probe light and the coupling light propagate in the opposite direction , In rubidium Rb In the atomic vapor chamber , Interact with atoms

• When there is no microwave , Observed Standard cascade three-level EIT Transparent peak
• When there is microwave field , Observed EIT Transparent peak , Split Into two peaks , spacing $\Delta f$

$${\Omega }_{MW}=2\pi \Delta f$$
among ${\Omega }_{MW}$ It's the Rabi frequency （ Coupled with microwave Rydberg Energy level ）

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Considering scanning probe light , Doppler correction factor is introduced when detuning ?, Then the intensity of microwave electric field ：
$$|E|=\frac{\hslash }{\mu }{\Omega }_{MW}=2\pi \frac{\hslash }{\mu }\frac{{\lambda }_p}{{\lambda }_c}\Delta f$$
among $\mu$ yes Rydberg Electric dipole moment of energy level ,${\lambda }_p$ Is the wavelength of detection light ,${\lambda }_c$ Is the wavelength of the coupling light

Convert the measurement of electric field strength into frequency measurement （ Because of all physical quantities , The frequency measurement accuracy is the highest ）

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be based on Rydberg Atomic technology

1.THz Field strength measurement

Durham University Weatheril The team used three photons Rydberg state EIT, Measured 0.634THz Terahertz field strength

scanning Rydberg Laser Detuning , Record the probe light transmission

When detecting the detuning of light 、 When the detuning of the coupling light is zero , The four level Hamiltonian is ：

$${\hat{H}}^{4-level}=\frac{\hslash }{2}\left(\begin{array}{cccc}0& {\Omega }_p& 0& 0\\ {\Omega }_p& 2{\Delta }_{1ph}& {\Omega }_c& 0\\ 0& {\Omega }_c& 2{\Delta }_{2ph}& {\Omega }_R\\ 0& 0& {\Omega }_R& 2({\Delta }_R+{\Delta }_{3ph})\end{array}\right)$$

among
${\Delta }_{1ph}=\vec{v}\cdot {\vec{k}}_p$
${\Delta }_{2ph}=\vec{v}\cdot ({\vec{k}}_p+{\vec{k}}_c)$
${\Delta }_{3ph}=\vec{v}\cdot ({\vec{k}}_p+{\vec{k}}_c+{\vec{k}}_R)$
$\vec{v}$ Is the atomic velocity
$k_p=2\pi /(852nm)$ Is the number of detected light waves ,${\Omega }_p$ It is the Rabi frequency of detection light
$k_c=2\pi /(1470)$ Is the number of coupled light waves ,${\Omega }_c$ Is the Rabi frequency of coupled light
$k_R=2\pi /(799nm)$ yes Rydberg Number of light waves ,${\Omega }_R$ yes Rydberg Optical Rabi frequency
${\Delta }_R$ yes Rydberg Light detuning

For further study EIT-AT split , introduce 0.634THz Field coupling $$21P_{3/2}\to 21S_{1/2}$$ bring EIT The window splits into two peaks

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After opening the terahertz field , Use double Lorentz linetype to fit data
Limit for each Lorenz peak Width , To match EIT Cleavage peak ,
The height of the peak 、 The bimodal spacing is set as a free parameter , Fit the curve
extract EIT The cleavage peak corresponds to THz Rabi frequency ${\Omega }_T/2\pi =(5.2\pm 1.4)MHz$,
It can be calculated that THz Field strength $(25\pm 5)mV\cdot c{m}^{-1}$

specific Rydberg States can only be coupled to a few terahertz frequencies close to resonance , But you can choose different Rydberg States to couple different frequencies , Realize the detection of wide terahertz frequency domain .

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2.THz Near field high-speed imaging

Convert the hard to detect terahertz signal into other easy to detect signals , For example, electrical signals

• In the early ： With spatial distribution THz Ionization Rydberg atom , The generated ions are focused on a spatially resolved microchannel plate , Realize to THz Spatially distinguishable detection of field strength （ shortcoming ： Yes Rydberg Atoms are destructive , Disposable , Low resolution ）
• 2016： use THz Pumping Rydberg atom , Through spontaneous emission , The fluorescence in the visible light band , Imaging —— Realized THz Near field real-time imaging of spatial distribution of field strength

Infrared laser beam and THz Beam coaxial alignment , Through the 2 mm Long quartz saturated bubbles

At the spatial overlapping position of terahertz field and laser beam, the atom is excited to $21S_{1/2}$ Of Rydberg state , And emit fluorescence in the visible light band

The laser beam and terahertz wave pass horizontally through the imaging area , Some terahertz waves are reflected to produce standing wave interference structures

This imaging technology does not require repeated data acquisition or scanning
Detector location , So imaging is real-time . The bandwidth limit of imaging is determined by Rydberg Energy level lifetime determines , Generally about Microsecond Magnitude

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Using high-speed rotating optical chopper （ Rotating blade with adjustable frequency ）, It can verify the high-speed performance of the imaging system

• Reduce the thickness of cesium bubble chamber + Enhance anti reflection layer , Sure Improve image quality
• The more advanced THz lens, Sure Improve image resolution
• Enlarge the cesium bubble chamber to expand THz Area of Sensor , Form a larger atomic excitation surface , Increase the imaging area

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3.THz signal communication

• Compared with microwave communication , Large bandwidth 、 Large capacity
• Compared with laser communication , For platform stability 、 Low requirements for follow-up

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The picture below is Rydberg Atomic digital communication experimental device and energy level system

Connect baseband digital signal with Rydberg Microwave mixing of atomic resonance （ The sender ）

Microwave signal absorption mixing occurs EIT-AT split , Will receive Band signal Converted to probe light Amplitude phase ${\phi }_{\mu }$

External use heterodyne probe , Phase demodulation is carried out through the lock-in amplifier
${\phi }_{\mu }=arctan(V_Q/V_I)$
take Phase information Turn into Quadrature phase change voltage signal

（f） The demodulated co directional voltage signal is given $V_I$ Examples with five different coding phases

（g）（h） It is the phase signal and phase trajectory of the signal receiving end （8PSK）

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Rydberg atom Antenna

The following is based on a four level atomic system THz Communication scheme

$6S_{1/2}(F=4)$ Of Cs The atom is in $|1*$
$6P_{3/2}(F^{\prime }=5)$ Of Cs The atom is in $|2*$
$25S_{1/2}(F^{\prime }=5)$ Of Cs The atom is in $|3*$
$25P_{3/2}(F^{\prime }=5)$ Of Cs The atom is in $|4*$

• Detection light wavelength $852nm$, coupling $|1*|2*$ Ecological transition , Corresponding to Rabi frequency ${\Omega }_p$
• Coupling light wavelength $515nm$, coupling $|2*|3*$ Ecological transition , Corresponding to Rabi frequency ${\Omega }_c$
• Use $338.75GHz$ Of THz site , For coupling two Rydberg state $|3*|4*$ Ecological transition , The corresponding Rabi frequency is ${\Omega }_T$

Four level Hamiltonian $H^{4-level}$ Expressed as
$$\begin{gathered} H=\hslash \{{\Omega }_p|1**2|+{\Omega }_c|2**3|+{\Omega }_T|3**4|- \\ {\Delta }_p|2**2|-({\Delta }_p+{\Delta }_c)|3**3|- \\ ({\Delta }_p+{\Delta }_c-{\Delta }_T)|4**4|+h.c.\} \end{gathered}$$

among
Rabi frequency
${\Omega }_p={\mu }_{12}{E}_p/\hslash$
${\Omega }_c={\mu }_{23}{E}_c/\hslash$
${\Omega }_T={\mu }_{34}{E}_T/\hslash$
Detuning
${\Delta }_p={\omega }_p-{\omega }_{12}$
${\Delta }_c={\omega }_c-{\omega }_{23}$
${\Delta }_T={\omega }_T-{\omega }_{34}$
The detection light is a weak field , When ${\Omega }_c=2\pi \times 5.72MHz$,THz Rabi frequency ${\Omega }_T=2\pi \times [0,1,2.5,5]MHz$ when ,EIT-AT The split result is shown in the right figure （b）

Yes THz The carrier is amplitude modulated AM, Got EIT The signal will also have modulation information

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Purpose + Conclusion

Rydberg Atoms have great electric dipole moments in the microwave and terahertz bands , Using the quantum interference effect, the electromagnetic wave field strength of this frequency band can be Highly sensitive detection , Theoretically, the sensitivity can be much higher than that of the existing detection technology

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problem

Rydberg What structure is used for atomic antenna ？

On the left vector of Quantum States 、 How is the right vector calculated ？

The function and significance of Hamiltonian ？
Is the sum of the kinetic energy of all particles plus the potential energy of the particles related to the system
For different cases or numbers of particles , Hamiltonian is different

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