Atom Interferometers
Cold atoms and ultra-cold atoms have relatively longer de Broglie wavelengths. Using cold atoms can increase the spacing of atom interference fringes, making it easier to observe the interference characteristics of matter waves. Since 1991, atom interferometers have been widely used in geodesy, inertial navigation, tests of general relativity, determination of fundamental physical constants, and more. Gravity measurement instruments have extensive applications in resource exploration and environmental surveying. Currently, a common type of atomic interferometer is the stimulated Raman transition-based atomic interferometer, which uses the stimulated Raman process to achieve coherent manipulation of atomic wave packets. Depending on the sequence of Raman laser pulses, cold atom interferometers can be classified into two main types: Ramsey-Bordé type and Mach-Zehnder (M-Z) type.
Stimulated Raman Transition
The stimulated Raman transition process can be explained using a three-level atomic model. As shown in Figure 1, single-mode laser fields ω₁ and ω₂ couple the two ground states |1〉, |3〉 and one excited state |2〉 of the atom, forming a coherent stimulated Raman transition. Through the stimulated Raman transition, the transfer of atomic population between different ground states can be achieved. The population transfer between states is jointly determined by the effective Rabi frequency (Ω_R), the two-photon detuning (δ), and the interaction time (τ). This process is analogous to the Rabi oscillation process between a microwave field and a two-level system. An atom initially in ground state |1〉 undergoes a stimulated Raman transition to ground state |3〉. When the Raman laser intensity is scanned, the population of atoms in state |3〉 exhibits Rabi oscillations, which follow a sinusoidal curve. The decay of the Rabi oscillations is caused by the non-uniform intensity distribution of the Raman light and the velocity distribution of the atoms. The period of the Rabi oscillation depends on the direction of the magnetic field. The pulse corresponding to half the atomic population transferring to state |3〉 is called a π/2 pulse, and the pulse corresponding to the entire atomic population transferring to state |3〉 is called a π pulse. During the stimulated Raman optical transition, the transfer of atomic population is accompanied by a change in the atomic recoil momentum.
Fig. 1 The process of stimulated Raman transition in a three-level atom.
Ramsey-Bordé Atom Interferometer
A cold atom Ramsey-Bordé interferometer can be implemented using the stimulated Raman transition process with a π/2 - π/2 Raman laser pulse sequence. A typical experimental scheme for a Ramsey-Bordé type atom interferometer is shown in Figure 2. Atoms initially in state |1〉 are first subjected to a π/2 pulse of Raman light. After a period of free evolution (time T), they are then subjected to a second π/2 pulse of Raman light. The population of atoms in state |3〉 subsequently exhibits Ramsey-Bordé interference fringes.
Fig. 2 Experimental scheme of a Ramsey-Bordé atomic interferometer.
Mach-Zehnder (M-Z) Atom Interferometer
The Mach-Zehnder (M-Z) atom interferometer is realized using a π/2–π–π/2 Raman pulse sequence. As shown in Figure 3, when atoms initially in the |1⟩ state are split by the first Raman pulse, there is a 50% probability for the atoms to remain in the |1⟩ state and a 50% probability to transition to the |3⟩ state. Atoms in the |3⟩ state simultaneously acquire the laser phase φ₁, forming a coherent superposition state. When the atoms interact with the second Raman pulse, they undergo a π transition, exchanging populations between the states while acquiring the laser phase φ₂. Upon interaction with the third Raman pulse, atoms in the |1⟩ state have a 50% chance of remaining in |1⟩ and a 50% chance of transitioning to |3⟩. Similarly, atoms in the |3⟩ state have a 50% chance of remaining in |3⟩ and a 50% chance of transitioning to |1⟩. All atoms acquire the laser phase φ₃ during this process. Thus, after interacting with the three Raman pulses, the internal states of the atoms change. The variation in the internal state population depends on the phases of the Raman lasers. By scanning the phase of any one of the Raman lasers, atomic interference fringes can be observed.
Fig. 3 Schematic diagram of a Mach-Zehnder atomic interferometer.