A method for rapid cooling of ionic crystals based on EIT

Abstract

The present invention provides a method for rapidly cooling an ion crystal based on EIT, which belongs to the field of ion cooling. The method comprises: S1: pre-treating trapped ions in an ion trap; S2: using a first light beam and a second light beam to simultaneously irradiate the trapped ions and maintain for a preset time; S3: characterizing the average number of phonons of the trapped ions obtained in step S2, and if the average number of phonons does not meet the preset conditions, repeating step S2; S4: ending cooling to obtain an ion crystal that meets the requirements. The present invention reduces the system's requirements for laser stability by adjusting the first light beam (coupling light) and the second light beam (probe light) used for EIT cooling to meet non-strict conditions, increases the cooling bandwidth by generating non-resonant drive, reduces the relaxation time of the system cooling process due to the detuning difference between the coupling light and the probe light, and accelerates the cooling process; and further improves the cooling rate by periodically modulating the Rabi frequency of the coupling light.

Description

Technical Field

[0001] The invention belongs to the field of ion cooling, and in particular relates to a method for rapidly cooling an ion crystal based on EIT. Background Art

[0002] When cooling large-scale ions, due to the presence of ions with different motion modes in the system, traditional cooling methods usually cool a specific motion mode and cannot cover all motion modes at the same time, thus limiting the cooling bandwidth; secondly, in the ion cooling method, different motion modes need to be cooled sequentially, thus limiting the cooling rate. In the existing technology, electromagnetic induced transparent cooling (EIT Cooling) can achieve wide-band cooling while maintaining a low cooling limit because it couples the excited state with a wide linewidth ( ). In standard EIT cooling, the bandwidth of EIT cooling is mostly broadened by reducing the detuning of the cooling beam, but this ignores the fact that this may deteriorate the cooling effect (cooling rate and cooling limit). Therefore, how to broaden the cooling bandwidth while improving the cooling effect is a technical problem to be solved in ion cooling. Summary of the invention

[0003] Based on this, the technical solution provided by the present invention, based on the traditional EIT cooling technology, adjusts the detuning amount of the coupling light and the detection light in the three-level system to meet the non-strictly equal condition, and modulates the periodic change of the Rabi frequency of the coupling light, thereby improving the cooling rate of the large-scale ion crystal in the ion trap.

[0004] In order to achieve the above object, the present invention provides a method for rapidly cooling an ionic crystal based on EIT, the method comprising:

[0005] S1: pre-processing the trapped ions in the ion trap;

[0006] S2: using the first light beam and the second light beam to irradiate the trapped ions simultaneously and maintaining the irradiation time for a preset time;

[0007] S3: characterizing the average phonon number of the trapped ions obtained in step S2, and if the average phonon number does not meet a preset condition, repeating step S2;

[0008] S4: end cooling and obtain an ionic crystal that meets the requirements;

[0009] The energy levels of the trapped ions include a first Zeeman sub-level, a second Zeeman sub-level, an excited state level, and a metastable state level, the energy of the first Zeeman sub-level is higher than the energy of the second Zeeman sub-level; the first light beam and the second light beam satisfy the following conditions:

[0010] ,

[0011] is the modulation Rabi frequency of the first light beam, is the detuning amount of the first beam, is the detuning amount of the second beam, is the trapping frequency of the ion trap, and t is the time.

[0012] Specifically, step S2 further includes: using an acousto-optic modulator to modulate the first light beam so that the Rabi frequency satisfies the following condition:

[0013] ,

[0014] is the reference value of the Rabi frequency, is the modulation amplitude of the Rabi frequency, is the modulation frequency of the Rabi frequency.

[0015] Specifically, step S1 specifically includes: using Doppler cooling to make the average phonon number of the trapped ions less than twenty.

[0016] Preferably, step S2 further comprises: setting the trapped ions to calcium ions; setting the first light beam to a blue detuned wavelength of 397 nm. - polarized light, so that the calcium ions resonate transition between the first Zeeman sub-energy level and the excited state energy level; the second light beam is set to be 397nm blue detuned π-polarized light, so that the calcium ions resonate transition between the second Zeeman sub-energy level and the excited state energy level.

[0017] Furthermore, step S3 specifically includes: using a third light beam to irradiate the trapped ions obtained in step S2 to make the trapped ions transition from the ground state to the metastable state; using a spectral analysis instrument to detect the sideband spectrum of the transition from the ground state to the metastable state, and obtaining the average phonon number of the trapped ions by fitting the sideband spectrum with the analytical solution of the sideband Rabi oscillation; wherein the third light beam is 729nm π-polarized light.

[0018] Preferably, 100-150 or 120-170 as the preset time.

[0019] Specifically, the preset condition is that the average phonon number of the trapped ions is less than 0.1.

[0020] The beneficial effects achieved by the present invention through the above technical solution are:

[0021] 1) By adjusting the first light beam (coupling light) and the second light beam (probe light) used for EIT cooling to meet non-strict conditions, not only the system's requirements for laser stability are reduced, the system complexity is reduced, but also the ion phonon modes that can be covered by the cooling laser are increased by generating non-resonant drive, thereby increasing the cooling bandwidth. More importantly, due to the difference in detuning between the coupling light and the probe light, the relaxation time of the system during the cooling process is reduced, thereby accelerating the cooling process.

[0022] 2) By periodically modulating the Rabi frequency of the coupled light, Floquet side bands are introduced, which increases the interaction between the cooling beam and the multiple motion modes of the ions, further improving the cooling rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 The embodiment of the present invention Schematic diagram of the energy level structure of ions and the EIT cooling architecture.

[0024] Figure 2 Schematic diagram of the structure of an EIT cooling device according to an embodiment of the present invention.

[0025] Figure 3 Schematic diagram of the ion ground state cooling process according to an embodiment of the present invention.

[0026] Figure 4 It is a comparison diagram of the cooling effect of the embodiment of the present invention and the traditional EIT cooling. DETAILED DESCRIPTION

[0027] In order to make the purpose, technical solution and advantages of the present invention more clear, the specific implementation of the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the embodiments described herein are only used to explain the present invention, but are not used to limit the scope of the present invention.

[0028] The method for rapidly cooling an ionic crystal based on EIT in an embodiment of the present invention comprises the following steps:

[0029] S1: pre-treating the trapped ions in the ion trap; S2: irradiating the trapped ions with the first light beam and the second light beam simultaneously and maintaining the irradiation time; S3: characterizing the average phonon number of the trapped ions obtained in step S2, if the average phonon number of the trapped ions does not meet the preset conditions, repeating step S2; S4: ending the cooling to obtain an ion crystal that meets the requirements.

[0030] Exemplarily, the energy levels of the trapped ions include a first Zeeman sub-level, a second Zeeman sub-level and an excited state level, and the energy of the first Zeeman sub-level is higher than the energy of the second Zeeman sub-level; the first light beam and the second light beam are set to meet the conditions, which can ensure that the EIT cooling process can bring the phonons close to the zero phonon state in the shortest time. In the embodiment of the present invention, the first light beam and the second light beam meet the following conditions:

[0031] ,

[0032] in, is the Rabi frequency of the first beam, is the detuning amount of the first beam, is the detuning amount of the second beam, is the trapping frequency of the ion trap, and t is the time.

[0033] In the above steps, step S1 specifically includes:

[0034] 1) Apply a constant magnetic field to the trapped ions in the ion trap, so that the ground state energy level of the trapped ions is divided into the first Zeeman sub-level and the second Zeeman sub-level. Specifically, a constant magnetic field is applied to the trapped ions in the ion trap, and the direction of the constant magnetic field is 45° to the axial direction of the ion trap. Then, the internal energy levels of the ions that can produce the EIT structure are selected, which are the second Zeeman sub-level , the first Zeeman sublevel and excited state energy levels .

[0035] 2) Doppler cooling is used to reduce the average number of phonons in the trapped ions to less than 20. Specifically, a 397 nm beam is used to irradiate the trapped ions for approximately 1000 During Doppler cooling, since the ion radiation line width is greater than its macroscopic motion frequency, its limit temperature is determined by this line width or photon recoil velocity. After Doppler cooling, the average number of phonons of the trapped ions is less than twenty. In one or other embodiments of the present invention, after Doppler cooling, the average number of phonons of the trapped ions is reduced to approximately ten.

[0036] See also Figure 1 , Figure 1 The embodiment of the present invention Schematic diagram of the internal energy level structure of ions and the EIT cooling architecture. The first light beam and the second light beam are used to irradiate the trapped ions simultaneously and maintain the time for a preset time. Specifically, the embodiment of the present invention adopts 100-150 or 120-170 , as the preset time for the first light beam and the second light beam to simultaneously irradiate the trapped ions and maintain. Step S2 specifically includes:

[0037] 1) Set the trapped ion to calcium ion.

[0038] 2) Set the second beam to be a 397nm blue detuned π-polarized light to make the calcium ions at the second Zeeman sublevel and excited state energy levels Resonance transition.

[0039] 3) Set the first beam to a blue detuned σ of 397 nm - Polarized light is used to make calcium ions at the first Zeeman sublevel and excited state energy levels In particular, the first light beam is modulated using an acousto-optic modulator so that the Rabi frequency satisfies the following conditions:

[0040] ,

[0041] in, is the reference value of the Rabi frequency, is the modulation amplitude of the Rabi frequency, is the modulation frequency of the Rabi frequency.

[0042] In particular, step S3 specifically includes:

[0043] 1) Using the third light beam to irradiate the trapped ions obtained in step S2, the trapped ions are moved from the ground state energy level to Transition to metastable state In particular, the third light beam used in the embodiment of the present invention is 729nm Polarized light, used to prepare the internal state of ions to metastable energy levels .

[0044] 2) Use spectral detection instruments to detect the ground state energy level Transition to metastable state The sideband spectrum of The electric quadruple transition sideband spectrum between them is fitted with the analytical solution of the sideband Rabi oscillation to obtain the average phonon number of the trapped ion.

[0045] Exemplarily, in the embodiment of the present invention, cooling is terminated when the average phonon number of the trapped ions is less than 0.1.

[0046] Embodiment 2

[0047] On the basis of the first embodiment, the second embodiment of the present invention also includes a device for rapidly cooling ionic crystals based on EIT, see Figure 2 , Figure 2 Schematic diagram of the structure of the EIT cooling device used in the embodiment of the present invention. Figure 2It can be seen that the EIT cooling device used in the embodiment of the present invention includes a trapping unit, a magnetic field unit, a cooling unit and a detection unit.

[0048] Trapped cell: The ions used in the embodiment of the present invention are , trapped in an ion trap, the axial trapping frequency of the trap is MHz, the radial trapping frequency is MHz. Ion ground state energy level , excited state energy level The natural line width is MHz.

[0049] Magnetic field unit: The steady magnetic field strength used in the embodiment of the present invention is , the angle between the magnetic field direction and the axial direction of the trap is 45°. Under this magnetic field, the ground state energy level of the ion will split into two Zeeman sub-levels: the first Zeeman sub-level and the second Zeeman sublevel (energy level difference is 15.36MHz), thus the excited state energy level form Type energy level structure.

[0050] Cooling unit: mainly includes the first beam and the second beam of 397nm, with different polarization and intensity. The first beam is blue detuned Polarized light, the detuning amount is recorded as ( MHz), the Rabi frequency is recorded as , for coherently driven first Zeeman sublevel of the ground state and excited state energy level The second beam is blue detuned Polarized light, the detuning amount is recorded as , the Rabi frequency is denoted as , for coherently driving the second Zeeman sublevel of the ground state and excited state energy level In order to meet the electromagnetically induced transparency condition, the Rabi frequencies of the first and second beams need to satisfy relationship.

[0051] Detection unit: mainly includes A polarized third beam is used to pump the ions from the ground state to the metastable state . Quadrupole transition measured at 729nm In one or other embodiments of the present invention, before using the third light beam, a beam with a polarization of The 397nm laser pulse has a duration of 50 , used to prepare the internal state of the ion to the second Zeeman sublevel .

[0052] Embodiment 3

[0053] On the basis of the first and second embodiments, the embodiment of the present invention also includes a method and steps for setting the parameters of the cooling beam.

[0054] See also Figure 3 , Figure 3 is a schematic diagram of the cooling process of the ion ground state. Figure 3 It can be seen that the method for rapidly cooling an ionic crystal based on EIT according to an embodiment of the present invention comprises the following steps:

[0055] First, the internal state of the ion is prepared at the first Zeeman sublevel of the ground state or the second Zeeman sublevel Then it transitions to the excited state energy level through the blue sideband, while the phonon state decreases by one, and finally returns to the ground state energy level through spontaneous radiation. , the atomic internal state returns to the ground state energy level, but the number of phonons increases from becomes , the cooling target is achieved. As the sub-process continues to cycle, the cooling limit is finally reached ( ), thereby achieving ground-state cooling of the ion motion mode.

[0056] The sub-processes of the above process are considered separately to obtain the optimal parameter conditions. Considering that the entire cooling process is an open quantum system, the process can be described by the master equation ,in is the Liouville super operator, and its matrix form is:

[0057] ,

[0058] Among them, the Hamiltonian , is the jumping operator, which describes the spontaneous radiation process of ions; Excited state energy level The spontaneous emission rate, ground state energy level and excited state energy levels The transition frequency between , the transition between the two energy levels has a frequency of The laser field is driven by the Rabi frequency. , Detuning . is the trapping frequency of the well, is the annihilation (creation) operator of phonons; is the effective interaction between phonons and the internal states of ions, is the Lamb-Dicke parameter. , the red sideband transition is close to resonance, while the large detuned carrier transition will give the energy level Bringing AC Stark Shift .

[0059] Find the eigenvalue expression of the Liouville matrix, arranged from largest to smallest in terms of real part, , where the first eigenvalue corresponds to the steady state of the system, and the real part of the second eigenvalue describes the instantaneous relaxation rate of the system, also known as the Liouville energy gap , whose reciprocal is the relaxation time of the system Therefore, the larger the Liouville energy gap corresponding to the cooling process, the faster the cooling rate. The maximum energy gap condition obtained is .

[0060] For EIT cooling, simply replace the beam parameters here as follows , , and ignore Then, we can substitute the high-order small quantity of , and then bring in the maximum energy gap condition to obtain the fastest cooling rate condition: In one or other embodiments of the present invention, the condition with the fastest cooling rate is .

[0061] The above conditions and traditional EIT cooling require two-photon resonance Different, because the cooling resonance in the embodiment of the present invention can be achieved by AC Stark frequency shift and the detuning difference between the first and second beams This not only provides a wider cooling bandwidth, but also does not require additional energy levels. In this way, embodiments of the present invention can use a series of cooling beams with different detuning to perform simultaneous cooling of multiple modes regardless of their mode spacing. Embodiments of the present invention can be tuned to a cooling range of more than 5 MHz.

[0062] By setting the parameters of the cooling laser according to this parameter condition, the EIT cooling rate can be maximized. Moreover, this condition breaks the strict cooling requirements of standard EIT cooling, so in principle, any range of motion mode spectra can be cooled simultaneously.

[0063] The parameters of the first and second beams are set as follows: First, the first beam is blue-detuned Polarized light, energy level and energy level coupling, resulting in two dressed states Then modulate Detuning of polarized light and Close and meet Under this condition, the energy level A red-sideband resonance in the strict sense is produced between the two, thereby reducing the number of phonons in the most efficient way.

[0064] A method provided in an embodiment of the present invention is to adjust parameters such as the Rabi frequency and detuning amount of the cooling beam to satisfy a specific relationship, which not only breaks the strict cooling requirements of standard EIT cooling and broadens the EIT cooling bandwidth, but also can achieve the cooling purpose in the shortest time, thereby providing a new technology for ion cooling.

[0065] See also Figure 4 , Figure 4 This is a comparison chart of the cooling effect of the embodiment of the present invention and traditional EIT cooling. In the figure, the horizontal axis is the cooling time, and the vertical axis is the average number of phonons of trapped ions. The results show that compared with traditional EIT cooling, the method of the embodiment of the present invention achieves a lower cooling limit in a shorter time, which means that compared with traditional EIT cooling, the method of the embodiment of the present invention can achieve a better cooling effect.

[0066] Finally, it should be noted that the above specific implementation methods are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the spirit and scope of the technical solution of the present invention, which should be included in the scope of the claims of the present invention.

Claims

1. A method for rapidly cooling an ionic crystal based on EIT, characterized in that: The method comprises: S1: pre-processing the trapped ions in the ion trap; S2: using the first light beam and the second light beam to irradiate the trapped ions simultaneously and maintaining the irradiation time for a preset time; S3: characterizing the average phonon number of the trapped ions obtained in step S2, and if the average phonon number does not meet a preset condition, repeating step S2; S4: ending cooling to obtain an ionic crystal that meets the requirements; in, The energy levels of the trapped ion include a first Zeeman sub-energy level, a second Zeeman sub-energy level and an excited state energy level, and the energy of the first Zeeman sub-energy level is higher than the energy of the second Zeeman sub-energy level; The first light beam and the second light beam satisfy the following conditions: ， is the Rabi frequency of the first beam, is the detuning amount of the first beam, is the detuning amount of the second beam, is the trapping frequency of the ion trap, and t is the time.

2. The method according to claim 1, characterized in that Step S2 also includes: using an acousto-optic modulator to modulate the first light beam so that the Rabi frequency satisfies the following condition: ， is the reference value of the Rabi frequency, is the modulation amplitude of the Rabi frequency, is the modulation frequency of the Rabi frequency.

3. The method according to claim 1, characterized in that Step S1 specifically includes: using Doppler cooling to make the average phonon number of the trapped ions less than twenty.

4. The method according to claim 3, characterized in that Step S2 also includes: Setting the trapped ion to be a calcium ion; Set the first beam to a blue detuned value of 397 nm. - polarized light to cause the calcium ions to resonantly transition between the first Zeeman sub-energy level and the excited state energy level; The second light beam is set to be a 397nm blue detuned π-polarized light, so that the calcium ions undergo a resonant transition between the second Zeeman sub-energy level and the excited state energy level.

5. The method according to claim 4, characterized in that Step S3 specifically includes: irradiating the trapped ions obtained in step S2 with a third light beam, so that the trapped ions transition from the second Zeeman sub-energy level to a metastable energy level; Using a spectrum analyzer to detect the sideband spectrum of the trapped ion transitioning to the metastable energy level, fitting the sideband spectrum with the analytical solution of the sideband Rabi oscillation to obtain the average phonon number of the trapped ion; Wherein, the third light beam is 729nm π-polarized light.

6. The method according to claim 1, characterized in that Use 100-150 or 120-170 as the preset time.

7. The method according to claim 1, characterized in that The preset condition is that the average phonon number of the trapped ions is less than 0.1.

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