CN112254830A - Method and device for BEC spin quantum weak measurement - Google Patents
Method and device for BEC spin quantum weak measurement Download PDFInfo
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Abstract
The invention relates to a method and a device for weak measurement of BEC spin quantum. The device includes: a microwave horn, BEC state cold atoms, an anti-Helmholtz coil and a CCD camera. The method comprises the steps of utilizing microwaves radiated by a microwave waveguide to prepare cold atoms in a BEC state in vacuum equipment to a superposition state, utilizing Stern-Gerlach measurement to generate a first atomic group with two groups of atoms having larger superposition, utilizing a microwave horn, an anti-Helmholtz coil and the Stern-Gerlach measurement to separate the first atomic group into two groups of second atomic groups without superposition, but two groups of atoms in each group still have larger partial superposition, and selecting a target atomic group through a CCD camera to absorb and image to obtain a spin value. The scheme is based on the technology of ultra-cold BEC atomic manipulation, the characteristic that the atomic spin state can be rapidly changed by microwaves is utilized, the radical is split and interfered by a Stern-Gerlach device, the displacement of the mass center of the radical relative to the central position can be amplified and improved, and the sensitivity of the BEC ultra-cold atomic spin measurement is measured.
Description
Technical Field
The invention relates to the technical field of weak signal measurement, in particular to a method and a device for BEC spin quantum weak measurement.
Background
Before half a century, the theoretical research on quantum weak measurement process was first conducted, and the abnormal measurement result is called weak value and shows extraordinary characteristics, thereby leading to extensive discussion. In a conventional study using weak measurement, a weak value-based protocol is proposed to directly measure a wave function of a quantum state. The method has been used to measure the spatial wave function of photons and thus the quantum state, orbital angular momentum, trajectory, non-exchanged observables, or even quantum processes of photon polarization. However, up to now, spin measurements of BEC in mass particle systems have not been achieved experimentally. The reason is that in the Stern-Gerlach device for weak measurement in the experimental process, because the spin direction of atoms cannot be transited by two groups of coils, namely the SGx and the SGz, and a slowly rotating transition region occurs, the measurement accuracy cannot reach the expectation, the deeper physical research is difficult to be promoted, and the Stern-Gerlach device is difficult to control.
Disclosure of Invention
In order to overcome the problems in the related art, the invention provides a method and a device for weak measurement of BEC spin quantum, thereby solving the problem of difficult control of a Stern-Gerlach device and measuring the spin value of the BEC atomic group by using the centroid offset distance of the cold atomic group.
According to a first aspect of embodiments of the present invention, there is provided a method for weak measurement of BEC spin quanta, comprising the steps of:
s1: preparing cold atoms in a BEC state in vacuum equipment to a superposition state by using microwaves radiated by a horn-shaped microwave waveguide, and then closing the microwaves;
s2: using a magnetic field generated by an anti-Helmholtz coil to perform weaker Stern-Gerlach measurement along the z direction, so that two groups of atoms with different spin states are separated into two atomic groups, but the two groups of atoms are still overlapped by a larger part, and the atomic groups are first atomic groups;
s3: the microwave radiated by the horn-shaped microwave waveguide acts on the first atomic group, and the microwave is turned off after the spin state of the first atomic group is changed;
s4: performing conventional Stern-Gerlach measurement along the z direction by using a magnetic field generated by an anti-Helmholtz coil, so that the first atomic group is separated into two groups of atomic groups which are not overlapped, but the two groups of atoms in each group are still overlapped to a larger extent, and the two groups of atoms are the second atomic group;
s5: and selecting a target atomic group with a small atomic number from the two second atomic groups through a CCD camera, performing absorption imaging on the target atomic group, and calculating through the centroid of the target atomic group to obtain a spin value.
In one embodiment, preferably, in the step S1, the microwave generated in the horn-shaped microwave waveguide is an electromagnetic wave; the wavelength of the microwave is between that of infrared rays and radio waves; the frequency of the microwave is 6.832526409 GHz; wherein, the frequency generation process of the microwave is as follows:
s101: generating a 6.8GHz signal by a phase-locked loop;
s102: mixing a frequency signal by using a mixer, wherein the frequency of the mixed frequency signal is 32.526409 MHz;
s103: a signal having a frequency of 6.832526409GHz is formed as the frequency of the microwave.
In one embodiment, preferably, in the step S1, the BEC-state cold atom is Rb87An atom, the cold atomic energy level transition of said BEC state being | F ═ 1, mF＝-1＞→|F＝1，mF＝0＞；
The vacuum equipment is a glass vacuum cavity; the cold atoms of the BEC state are prepared by the microwaves
After the atoms are in the superposed state, the microwave is closed through the horn-shaped microwave waveguide;
the preparation conditions of the BEC state cold atoms are as follows:
the temperature of the cold atoms of the BEC state is 75 nk;
the purity of the cold atoms in the BEC state is more than 90%;
the number of atoms of the cold atoms of the BEC state is 1.5 x 105；
The critical temperature of the cold atoms of the BEC state satisfies the following first calculation formula:
wherein, TCIs the critical temperature, n is the particle density, m is the mass of each boson,
the reduced Planck constant (Dirac constant), pi is 3.1415926, kBZeta is a Riemann zeta function, and is a Boltzmann constant, and is 2.6124 taken as Zeta (3/2).
In one embodiment, preferably, in the step S2, the anti-helmholtz coil generates a gradient magnetic field in the z direction, and the atoms in the superimposed state generate two first clusters of atoms by using a Stern-Gerlach apparatus; the two first radicals are
And
two groups of atoms of (a); the microwave is turned off after the first radical is obtained.
In one embodiment, preferably, in step S3, the spin state of the two first clusters is transformed from | S > to | S' > and the quantization axis of the pseudo spin is rotated by 90 °.
In one embodiment, preferably, in the step S4, the anti-helmholtz coil has a total of 60 unidirectional coils, wherein each 20-turn coil is divided into three groups;
the number of the anti-Helmholtz coils is 2, the inner diameter of each anti-Helmholtz coil is 60mm, the outer diameter of each anti-Helmholtz coil is 140mm, and the distance between the two anti-Helmholtz coils is 83 mm;
the current of 200A can be passed through each group of coils, the longitudinal magnetic field gradient of 2.19Gs/cm/A is generated by each group of coils, and the transverse magnetic field gradient of 1.095Gs/cm/A is generated by each group of coils.
In one embodiment, preferably, in the step S5, the CCD/CMOS target surface size of the CDD camera is 1/3 inches, and each pixel of the CDD camera is 3.75 μm;
the process of obtaining spin values by centroid calculation of the target radical comprises:
s501: measuring a density distribution of BEC cold radicals from an image obtained by the CDD camera;
s502: fitting a centroid position according to the coordinates and gray values of each position of the pixels in the image;
s503: calculating the spin value of the target atomic group by using a second calculation formula according to the electric field intensity and the centroid position;
the spin state Ψ to be measured for the BEC in this scheme can be represented as: Σ ═ Σici|Ψi＞，|ΨiIs the spin operator
Of the eigenstates of (1), thus
So that the atom is at Ψ
The expectation of (2):
however, in real systems, it is difficult to measure ∑ si|ci|2·si.Thus, a pointer state is used to measure the expected value
The momentum ripple function of the BEC is chosen as the pointer state, so that the initial momentum state of the BEC can be written as
The Hamiltonian of the measurement process is
Therefore, expected value
Is converted into a measurement of the deviation of the waveform centroid position
The second calculation formula is:
therein, sigmai|ciφ(p-p0-gsi)|2Is a momentum probability distribution; g is the coupling strength or interaction strength; siIs composed of
The eigenvalues of (a); p is a radical ofiMomentum distribution as a function of wave; integral sum ofi|ciφ(p-p0-gsi)|2dp is the wave function probability distribution.
According to a second aspect of the embodiments of the present invention, there is provided an apparatus for BEC spin quantum weak measurement, including a microwave horn, BEC-state cold atoms, an anti-helmholtz coil, a CCD camera;
the microwave horn is used for generating a microwave electric field;
the cold atoms in the BEC state are placed in a vacuum device and used for observing results after different spin states;
the anti-Helmholtz coil generates a gradient magnetic field, and a Stern-Gerlach device is utilized to measure the cold atoms in the BEC state;
the CCD camera is used for selecting the cold atoms in the BEC state to carry out absorption imaging.
In one embodiment, preferably, the microwave horn, the cold atoms of the BEC state, the anti-helmholtz coil, and the CCD camera are all in an experimental coordinate system;
the experimental coordinate system comprises an x axis, a y axis and a z axis;
the three directions of the x axis, the y axis and the z axis are mutually vertical;
the transmitting direction of the microwave is incident at an angle of 45 degrees with the x axis and the y axis in the experimental coordinate system.
In one embodiment, preferably, the container of cold atoms in BEC state is a vacuum apparatus, which is a glass vacuum chamber; the vacuum degree of the vacuum apparatus was 8.6 x 10 without opening the cold atoms of the BEC state- 9pa, degree of vacuum of the vacuum apparatus in the case of opening the cold atoms of BEC state is 1.2 x 10-8pa。
According to a third aspect of embodiments of the present invention, there is provided an apparatus for BEC discretionary quantum weak measurement, comprising:
an atom preparation module 31 for preparing the cold atoms of the BEC state satisfying a preparation condition of a measurement method;
a first radical preparation module 32 for preparing the first radical;
a second radical preparation module 33 for preparing the second radical;
a target radical output module 34 for preparing the target radical by the CCD camera;
the processing and analyzing module 35 is configured to perform splitting width analysis of a raman absorption peak according to the captured image of the target atomic group;
and a weak value determination module 36 for obtaining the spin value through the centroid calculation of the target radical.
In one embodiment, preferably, the atom preparation module 31 is configured to:
judging whether the preparation condition of the BEC-state cold atoms is finished or not;
the preparation conditions of the BEC state cold atoms are as follows:
the temperature of the cold atoms of the BEC state is 75 nk;
the purity of the cold atoms in the BEC state is more than 90%;
the number of atoms of the cold atoms of the BEC state is 1.5 x 105；
The critical temperature of the cold atoms of the BEC state satisfies the following first calculation formula:
wherein, TCIs the critical temperature, n is the particle density, m is the mass of each boson,
the reduced Planck constant (Dirac constant), pi is 3.1415926, kBZeta is a Riemann zeta function, and is a Boltzmann constant, and is 2.6124 taken as Zeta (3/2).
Signaling a readiness completion of the cold atom in the BEC state after all readiness of the cold atom in the BEC state is satisfied.
In one embodiment, preferably, the first radical preparation module 32 is configured to:
receiving a readiness complete signal for the cold atom in the BEC state;
generating microwaves by using a microwave horn, wherein the microwaves generated in the microwave horn are electromagnetic waves; the wavelength of the microwave is between that of infrared rays and radio waves; the frequency of the microwave is 6.832526409 GHz. The cold atom in the BEC state is Rb87An atom, the cold atomic energy level transition of said BEC state being F ═ 1, mF＝-1＞→|F＝1，mF＝0＞；
The cold atoms of the BEC state are prepared by the microwaves
After the atoms are in the superposed state, the microwave is turned off through a microwave horn;
turning off the microwave after preparing the cold atoms in the BEC state in the vacuum equipment to the superposition state by using the microwave;
generating a gradient magnetic field in the z direction by using an anti-Helmholtz coil, and performing Stern-Gerlach measurement along the z direction to generate two first atomic groups which are divided according to the microwave proportion;
utilizing a Stern-Gerlach device to generate two groups of first atomic groups by the atoms in the superposed state; the two first radicals are
And
two groups of atoms of (a); and turning off the microwave after the first atomic group is obtained, and sending a first atomic group preparation completion signal.
In one embodiment, preferably, the second radical preparation module 33 is configured to:
after receiving the first radical preparation completion signal, turning on the microwave horn;
generating microwaves to act on the first atomic groups by using a microwave horn;
and turning off the microwave after the spin state of the first atomic group is changed, so that the quantization axis of the pseudo spin is rotated by 90 degrees.
And generating a magnetic field by using an anti-Helmholtz coil, and carrying out Stern-Gerlach measurement along the z direction to generate two completely separated second atomic groups and sending out a preparation completion signal of the second atomic groups.
In one embodiment, preferably, the target radical output module 34 is configured to:
selecting a target atomic group with a small atomic number from the two second atomic groups through a CCD camera;
and performing absorption imaging on the target atomic group, storing the imaging of the target atomic group into a readable storage medium, and sending a signal of finishing the storage of the target atomic group.
In one embodiment, preferably, the processing and analyzing module 35 is configured to:
acquiring a shot image of the target radical according to the received target radical storage completion signal;
analyzing the splitting width of the Raman absorption peak according to the shot image of the target atomic group;
calculating the electric field intensity of the microwave according to the splitting width;
the centroid position is fitted according to the coordinates and gray values of each position of the pixels in the image.
In one embodiment, preferably, the weak value determination module 36 is configured to:
calculating the spin value of the target atomic group by using a second calculation formula according to the electric field intensity and the centroid position;
the processor outputs spin values of the target radicals.
The spin state Ψ to be measured for the BEC in this scheme can be represented as: Σ ═ Σici|Ψi＞，|ΨiIs the spin operator
Of the eigenstates of (1), thus
Thus, the atom is at Ψ
The expectation of (2):
however, in real systems, it is difficult to measure ∑ si|ci|2·si.Therefore, we use a pointer state to measure the expected value
Selecting the momentum wave function of the BEC as a pointerThe initial momentum state of the BEC can thus be written as
The Hamiltonian of the measurement process is
Thus: expected value
Is converted into a measure of the displacement of the centroid position of the waveform.
The second calculation formula is:
therein, sigmai|ciφ(p-p0-gsi)|2Is a momentum probability distribution; g is the coupling strength or interaction strength; siIs composed of
The eigenvalues of (a); p is a radical ofiMomentum distribution as a function of wave; integral sum ofi|ciφ(p-p0-gsi)|2dp is the wave function probability distribution.
According to a fourth aspect of embodiments of the present invention, there is provided a computer-readable storage medium having stored thereon computer instructions which, when executed by a processor, implement the steps of the method of any one of the first aspects.
The technical scheme provided by the embodiment of the invention can have the following beneficial effects:
in the embodiment of the invention, according to the characteristic that microwave can rapidly change the spin state of atoms, the Stern-Gerlach device is used for splitting and interfering the atomic group, so that the purpose of deviating the mass center of the atomic group from the central position can be realized, the measurement of the spin state of the BEC supercooled atomic group is realized, and the method is simple and easy to realize; in addition, the scheme has the advantages of less interference on the spin state of the atoms to be subjected to ultra-cold treatment, independence on the physical size of a probe and the like, and is more suitable for the equipment development trend of miniaturization of devices.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present disclosure and together with the description, serve to explain the principles of the disclosure.
FIG. 1 is a flow chart of a method for weak measurement of BEC spin quanta according to one embodiment of the present invention.
Fig. 2 is a schematic diagram of the energy level structure of cold atoms in a method for weak measurement of BEC spin quanta according to an embodiment of the present invention.
Fig. 3 is a flow chart of a method for BEC spin quantum weak measurement according to one embodiment of the invention.
Fig. 4 is a schematic diagram of a theoretical simulation of a BEC atomic group to be measured for a method for weak measurement of BEC spin quanta in the present invention.
FIG. 5 is a flow chart of the computational acquisition of spin values in a method for weak measurement of BEC spin quanta according to one embodiment of the present invention.
Fig. 6 is a schematic structural diagram of an apparatus for weak measurement of BEC spin quanta according to an embodiment of the present invention.
FIG. 7 is a schematic block diagram of an apparatus for weak measurement of BEC spin quanta in accordance with an embodiment of the present invention.
The notation in the figures means: the method comprises the following steps of 1-a microwave horn, 2-an anti-Helmholtz coil, 3-BEC cold atoms, 4-a CCD camera, 31-an atom preparation module, 32-a first atom group preparation module, 33-a second atom group preparation module, 34-a target atom group output module, 35-a processing analysis module and 36-a weak value determination module.
Detailed Description
Reference will now be made in detail to the exemplary embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, like numbers in different drawings represent the same or similar elements unless otherwise indicated. The implementations described in the exemplary embodiments below are not intended to represent all implementations consistent with the present disclosure. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the present disclosure, as detailed in the appended claims.
According to the characteristic that microwave can rapidly change the spin state of atoms, the invention enables the atomic group to generate splitting and interference through a Stern-Gerlach device, and aims to deviate the mass center of the atomic group from the central position so as to measure the spin state of the BEC super-cooled atomic group, thereby providing a scheme for weak measurement of the BEC spin quantum.
FIG. 1 is a flow chart of a method for weak measurement of BEC spin quanta according to one embodiment of the present invention.
As shown in fig. 1, the present invention provides a method for weak measurement of BEC spin quantum, comprising the steps of:
s1: preparing cold atoms in a BEC state in vacuum equipment to a superposition state by using microwaves radiated by a horn-shaped microwave waveguide, and then closing the microwaves;
the microwave generated in the horn-shaped microwave waveguide is electromagnetic wave; the wavelength of the microwave is between that of infrared rays and radio waves; the frequency of the microwave is 6.832526409 GHz.
The cold atom in the BEC state is Rb87An atom, the cold atomic energy level transition of said BEC state being | F ═ 1, mF＝-1＞→|F＝1，m F0 >; as shown in fig. 2, in the present invention, the energy level structure of the cold atom describes | d > (| F ═ 1, m) with the spin downF1) and spin-up | u > (| F ═ 1, m F0 > or | F ═ 2, mF1), microwave pulses and
the energy difference between them resonates. The vacuum equipmentA glass vacuum cavity; the cold atoms of the BEC state are prepared by the microwaves
After the stacked state atoms are formed, the microwave is closed through the horn-shaped microwave waveguide.
Wherein it is clear that the cold atom is Rb87The atoms, corresponding to the energy transition process in the BEC state, provide a basis for experimental design of the wavelength of the frequency microwave of the corresponding microwave source. Under such conditions, the preparation of cold atoms in the BEC state by microwaves can be carried out so as to produce cold atoms with superposition of an upward spin and a downward spin.
Further, provision is made for the preparation of the cold atoms in the BEC state to be:
the temperature of the cold atoms of the BEC state is 75 nk;
the purity of the cold atoms in the BEC state is more than 90%;
the number of atoms of the cold atoms of the BEC state is 1.5 x 105；
The critical temperature of the cold atoms of the BEC state satisfies the following first calculation formula:
wherein, TCIs the critical temperature, n is the particle density, m is the mass of each boson,
the reduced Planck constant (Dirac constant), pi is 3.1415926, kBZeta is a Riemann zeta function, and is a Boltzmann constant, and is 2.6124 taken as Zeta (3/2).
S2: an anti-Helmholtz coil is used for generating a magnetic field, and weaker Stern-Gerlach measurement is carried out along the z direction, so that two groups of atoms with different spin states are separated into two atomic groups, but the two groups of atoms are still overlapped by a larger part, and the two groups of atoms are the first atomic group;
the anti-Helmholtz coil is at the z-directionGenerating a gradient magnetic field, and generating two groups of first atomic groups by utilizing the atoms in the superposed state by using a Stern-Gerlach device; the two first radicals are
And
two groups of atoms of (a); the microwave is turned off after the first radical is obtained.
S3: the microwave radiated by the horn-shaped microwave waveguide is applied to the first radical, and the microwave is turned off after the spin state of the first radical is changed.
The spin states of the two groups of atoms are transformed from | S > to | S' > and the quantization axes of the pseudo spins rotate by 90 degrees.
S4: performing conventional Stern-Gerlach measurement along the z direction by using a magnetic field generated by an anti-Helmholtz coil, so that the first atomic group is separated into two groups of atomic groups which are not overlapped, but the two groups of atoms in each group are still overlapped to a larger extent, and the two groups of atoms are the second atomic group;
s5: and selecting a target atomic group with a small atomic number from the two second atomic groups through a CCD camera, performing absorption imaging on the target atomic group, and calculating through the centroid of the target atomic group to obtain a spin value.
In this embodiment, under the preparation condition of the cold atoms in the BEC state, it is to be noted that in order to observe the result of interference after BEC is selected after different spin states pass, it is required that interference between substance waves of the selected cold atoms can occur, so that the atoms are prepared to the Bose-Einstein condensation state (Bose-Einstein condensation) BEC state. The bose-einstein theory predicts that when the temperature is ultra-low, the particles can enter the quantum state with the lowest energy, namely the wave functions of the particle matter waves entering the quantum state with the lowest energy are the same, so that the atoms required in the method are the preparation conditions of the cold atoms in the BEC state, and finally, the continuous separation of the cold state atomic groups is realized under the action of a gradient magnetic field.
Fig. 3 is a flow chart of a method for BEC spin quantum weak measurement according to one embodiment of the invention.
As shown in fig. 3, the frequency of the microwave is 6.832526409 GHz; wherein, the frequency generation process of the microwave is as follows:
s101: generating a 6.8GHz signal by a phase-locked loop;
s102: mixing a frequency signal by using a mixer, wherein the frequency of the mixed frequency signal is 32.526409 MHz;
s103: a signal having a frequency of 6.832526409GHz is formed as the frequency of the microwave.
In order to implement step S2, the anti-helmholtz coil has a total of 60 unidirectional coils, wherein each 20 coils is divided into three groups;
the number of the anti-Helmholtz coils is 2, the inner diameter of each anti-Helmholtz coil is 60mm, the outer diameter of each anti-Helmholtz coil is 140mm, and the distance between the two anti-Helmholtz coils is 83 mm;
the current of 200A can be passed through each group of coils, the longitudinal magnetic field gradient of 2.19Gs/cm/A is generated by each group of coils, and the transverse magnetic field gradient of 1.095Gs/cm/A is generated by each group of coils.
By this embodiment it is achieved that a gradient magnetic field is formed by 2 anti-helmholtz coils, while the cold atoms in superposition under the gradient magnetic field produce said first radicals of proportional microwave subdivision, but now the two radicals do not send a significant separation in space between said first radicals, with only a small displacement. Therefore, the subsequent steps S3 and S4 are required to convert the two groups of cold atoms into the second radicals, and the two groups of cold atoms are completely separated.
Fig. 4 is a schematic diagram of a theoretical simulation of a BEC atomic group to be measured for a method for weak measurement of BEC spin quanta in the present invention.
As shown in fig. 4, the theory of the present invention that can simulate the BEC radicals to be measured in advance selects an appropriate detuning amount Δ through experiments. By the method, a microwave electric field can be applied to the cold atoms, different microwaves generate different amplification factors, so that the spin state of the cold atoms is changed, the atomic groups are split and interfered through a Stern-Gerlach experiment, and the spin state of the BEC atomic group to be detected can be obtained by utilizing a CCD camera to absorb and image the mass center of one group of atoms.
FIG. 5 is a flow chart of the computational acquisition of spin values in a method for weak measurement of BEC spin quanta according to one embodiment of the present invention.
As shown in FIG. 5, the CCD/CMOS target size of the CDD camera is 1/3 inches, each pixel of the CDD camera is 3.75 μm;
the process of obtaining spin values by centroid calculation of the radicals includes:
s501: measuring a density distribution of BEC cold radicals from an image obtained by the CDD camera;
s502: fitting a centroid position according to the coordinates and gray values of each position of the pixels in the image;
s503: calculating the spin value of the target atomic group by using a second calculation formula according to the electric field intensity and the centroid position;
the spin state Ψ to be measured for the BEC in this scheme can be represented as: Σ ═ Σici|Ψi＞，|ΨiIs the spin operator
Of the eigenstates of (1), thus
So that the atom is at Ψ
The expectation of (2):
however, in real systems, it is difficult to measure ∑ si|ci|2·si.Therefore, weMeasuring expected value by using pointer state
The momentum ripple function of the BEC is chosen as the pointer state, so that the initial momentum state of the BEC can be written as
The Hamiltonian of the measurement process is
Thus: expected value
Is converted into a measurement of the deviation of the waveform centroid position
The second calculation formula is:
therein, sigmai|ciφ(p-p0-gsi)|2Is a momentum probability distribution; g is the coupling strength or interaction strength; siIs composed of
The eigenvalues of (a); p is a radical ofiMomentum distribution as a function of wave; integral sum ofi|ciφ(p-p0-gsi)|2dp is the wave function probability distribution.
The scheme is a method for weak measurement of BEC spin quantum, the Raman spectrometer CDD camera is used for capturing the image data of the atomic group which is clear and comprehensive enough, the center of mass is fitted according to the image data, the electric field intensity is calculated, and the calculation of the spin value of the atomic group is finally completed.
Fig. 6 is a schematic structural diagram of an apparatus for weak measurement of BEC spin quanta according to an embodiment of the present invention.
As shown in fig. 6, the device for BEC spin quantum weak measurement includes a microwave horn 1, BEC-state cold atoms 2, an anti-helmholtz coil 3, a CCD camera 4;
the microwave horn 1 is used for generating a microwave electric field;
the cold atoms 2 in the BEC state are placed in a vacuum device for observing the results after different spin states;
the anti-Helmholtz coil 3 generates a gradient magnetic field, and a Stern-Gerlach device is used for measuring the cold atoms in the BEC state;
the CCD camera 4 is used for selecting the cold atoms in the BEC state to carry out absorption imaging.
The microwave horn 1, the BEC-state cold atoms 2, the anti-Helmholtz coil 3 and the CCD camera 4 are all positioned in an experimental coordinate system;
the experimental coordinate system comprises an x axis, a y axis and a z axis;
the three directions of the x axis, the y axis and the z axis are mutually vertical;
the transmitting direction of the microwave is incident at an angle of 45 degrees with the x axis and the y axis in the experimental coordinate system.
The container of the BEC-state cold atoms 2 is vacuum equipment which is a glass vacuum cavity; the vacuum degree of the vacuum apparatus was 8.6 x 10 without opening the cold atoms 2 of the BEC state-9pa, the vacuum degree of the vacuum equipment is 1.2 x 10 under the condition of opening the cold atoms 2 of the BEC state-8pa。
The microwave horn 1 can use ADF4351 to generate a signal of 6.8GHz, and then mix the signal into 32.526409MHz by the mixer, and finally form a microwave source of 6.832526409 GHz.
The invention is used for BEC spin quantum weak measuring device, and has the main idea that the original spin state of atoms can rotate slowly by magnetic field, and has transition region, and the atoms can continuously expand the experimental device along with the increase of flight time, and can not meet the experimental purpose, so the invented device can have automatic calibration, has less interference to super-cold atom spin state, and does not depend on the physical size of the probe.
FIG. 7 is a schematic block diagram of an apparatus for weak measurement of BEC spin quanta in accordance with an embodiment of the present invention.
According to a third aspect of embodiments of the present invention, there is provided an apparatus for BEC discretionary quantum weak measurement, comprising:
an atom preparation module 31 for preparing conditions of the cold atoms of the BEC state;
a first radical preparation module 32 for preparing the first radical;
a second radical preparation module 33 for preparing the second radical;
a target radical output module 34 for preparing the target radical by the CCD camera;
the processing and analyzing module 35 is configured to perform splitting width analysis of a raman absorption peak according to the captured image of the target atomic group;
and a weak value determination module 36 for obtaining the spin value through the centroid calculation of the target radical.
Wherein the atom preparation module 31 is configured to:
judging whether the preparation condition of the BEC-state cold atoms is finished or not;
the preparation conditions of the BEC state cold atoms are as follows:
the temperature of the cold atoms of the BEC state is 75 nk;
the purity of the cold atoms in the BEC state is more than 90%;
the number of atoms of the cold atoms of the BEC state is 1.5 x 105；
The critical temperature of the cold atoms of the BEC state satisfies the following first calculation formula:
wherein, TCIs the critical temperature, n is the particle density, m is the mass of each boson,
the reduced Planck constant (Dirac constant), pi is 3.1415926, kBZeta is a Riemann zeta function, and is a Boltzmann constant, and is 2.6124 taken as Zeta (3/2).
And when the preparation conditions of the cold atoms in the BEC state are all satisfied, sending out a preparation condition completion signal of the cold atoms in the BEC state.
Wherein the first radical preparation module 32 is configured to:
receiving a readiness complete signal for the cold atom in the BEC state;
generating microwaves by using a microwave horn, wherein the microwaves generated in the microwave horn are electromagnetic waves; the wavelength of the microwave is between that of infrared rays and radio waves; the frequency of the microwave is 6.832526409 GHz. The cold atom in the BEC state is Rb87An atom, the cold atomic energy level transition of said BEC state being | F ═ 1, mF＝-1＞→|F＝1，mF＝0＞；
The cold atoms of the BEC state are prepared by the microwaves
After the atoms are in the superposed state, the microwave is turned off through a microwave horn;
turning off the microwave after preparing the cold atoms in the BEC state in the vacuum equipment to the superposition state by using the microwave;
generating a gradient magnetic field in the z direction by using an anti-Helmholtz coil, and performing Stern-Gerlach measurement along the z direction to generate two first atomic groups which are divided according to the microwave proportion;
utilizing a Stern-Gerlach device to generate two groups of first atomic groups by the atoms in the superposed state; the two first radicals are
And
two groups of atoms of (a); and turning off the microwave after the first atomic group is obtained, and sending a first atomic group preparation completion signal.
Wherein the second radical preparation module 33 is configured to:
after receiving the first radical preparation completion signal, turning on the microwave horn;
generating microwaves to act on the first atomic groups by using a microwave horn;
and turning off the microwave after the spin state of the first atomic group is changed, so that the quantization axis of the pseudo spin is rotated by 90 degrees.
And generating a magnetic field by using an anti-Helmholtz coil, and carrying out Stern-Gerlach measurement along the z direction to generate two completely separated second atomic groups and sending out a preparation completion signal of the second atomic groups.
Wherein the target radical output module 34 is configured to:
selecting a target atomic group with a small atomic number from the two second atomic groups through a CCD camera;
and performing absorption imaging on the target atomic group, storing the imaging of the target atomic group into a readable storage medium, and sending a signal of finishing the storage of the target atomic group.
Wherein the process analysis module 35 is configured to:
acquiring a shot image of the target radical according to the received target radical storage completion signal;
analyzing the splitting width of the Raman absorption peak according to the shot image of the target atomic group;
calculating the electric field intensity of the microwave according to the splitting width;
the centroid position is fitted according to the coordinates and gray values of each position of the pixels in the image.
Wherein the weak value determination module 36 is configured to:
calculating the spin value of the target atomic group by using a second calculation formula according to the electric field intensity and the centroid position;
the processor outputs spin values of the target radicals.
The second calculation formula is:
the spin state Ψ to be measured for the BEC in this scheme can be represented as: Σ ═ Σici|Ψi＞，|ΨiIs the spin operator
Of the eigenstates of (1), thus
So that the atom is at Ψ
The expectation of (2):
however, in real systems, it is difficult to measure ∑ si|ci|2·si.Therefore, we use a pointer state to measure the expected value
The momentum ripple function of the BEC is chosen as the pointer state, so that the initial momentum state of the BEC can be written as
The Hamiltonian of the measurement process is
Thus: expected value
Is converted into a measurement of the deviation of the waveform centroid position
The second calculation formula is:
therein, sigmai|ciφ(p-p0-gsi)|2Is a momentum probability distribution; g is the coupling strength or interaction strength; siIs composed of
The eigenvalues of (a); p is a radical ofiMomentum distribution as a function of wave; integral sum ofi|ciφ(p-p0-gsi)|2dp is the wave function probability distribution.
According to a fourth aspect of embodiments of the present invention, there is provided a computer-readable storage medium having stored thereon computer instructions which, when executed by a processor, implement the steps of the method of any one of the first aspects.
Through the technical scheme, according to the characteristic that the self-spinning state of atoms can be rapidly changed by microwaves, the radical is split and interfered by the Stern-Gerlach device, the purpose of deviating the mass center of the radical from the central position is realized, and the measurement of the self-spinning state of the BEC super-cooled radical is realized, so that the method is simple and easy to realize; in addition, the scheme has the advantages of automatic calibration, small interference on the spin state of the ultra-cold atoms, no dependence on the physical size of a probe and the like, is more suitable for the development trend of miniaturization of devices, and has a wider application scene.
It is further understood that the use of "a plurality" in this disclosure means two or more, as other terms are analogous. "and/or" describes the association relationship of the associated objects, meaning that there may be three relationships, e.g., a and/or B, which may mean: a exists alone, A and B exist simultaneously, and B exists alone. The character "/" generally indicates that the former and latter associated objects are in an "or" relationship. The singular forms "a", "an", and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.
It will be further understood that the terms "first," "second," and the like are used to describe various information and that such information should not be limited by these terms. These terms are only used to distinguish one type of information from another and do not denote a particular order or importance. Indeed, the terms "first," "second," and the like are fully interchangeable. For example, first information may also be referred to as second information, and similarly, second information may also be referred to as first information, without departing from the scope of the present disclosure.
It is further to be understood that while operations are depicted in the drawings in a particular order, this is not to be understood as requiring that such operations be performed in the particular order shown or in serial order, or that all illustrated operations be performed, to achieve desirable results. In certain environments, multitasking and parallel processing may be advantageous.
Other embodiments of the disclosure will be apparent to those skilled in the art from consideration of the specification and practice of the disclosure disclosed herein. This application is intended to cover any variations, uses, or adaptations of the disclosure following, in general, the principles of the disclosure and including such departures from the present disclosure as come within known or customary practice within the art to which the disclosure pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the disclosure being indicated by the following claims.
It will be understood that the present disclosure is not limited to the precise arrangements described above and shown in the drawings and that various modifications and changes may be made without departing from the scope thereof. The scope of the present disclosure is limited only by the appended claims.
Claims (10)
1. A method for weak measurement of BEC spin quanta, comprising the steps of:
s1: preparing cold atoms in a BEC state in vacuum equipment to a superposition state by using microwaves radiated by a horn-shaped microwave waveguide, and then closing the microwaves;
s2: performing Stern-Gerlach measurement of a first strength along the z direction by using a magnetic field generated by an anti-Helmholtz coil, so that two groups of atoms with different spin states are separated into two atomic groups to obtain a first atomic group, wherein an overlapped part is arranged between the two atomic groups;
s3: the microwave radiated by the horn-shaped microwave waveguide acts on the first atomic group, and the microwave is turned off after the spin state of the first atomic group is changed;
s4: performing Stern-Gerlach measurement of a second strength along the z direction by using a magnetic field generated by an anti-Helmholtz coil, so that the first atomic group is separated into two groups of atomic groups which are not overlapped, and a second atomic group is obtained;
s5: and selecting a target atomic group with a small atomic number from the two second atomic groups through a CCD camera, performing absorption imaging on the target atomic group, and calculating through the centroid of the target atomic group to obtain a spin value.
2. The method for weak measurement of BEC spin quantum according to claim 1, wherein in the step S1, the microwave generated in the horn-shaped microwave waveguide is an electromagnetic wave; the wavelength of the microwave is between that of infrared rays and radio waves; the frequency of the microwave is 6.832526409 GHz; wherein, the frequency generation process of the microwave is as follows:
s101: generating a signal of 6.8GHz by using a phase-locked loop;
s102: mixing a frequency signal by using a mixer, wherein the frequency of the mixed frequency signal is 32.526409 MHz;
s103: a signal having a frequency of 6.832526409GHz is formed as the frequency of the microwave.
3. The method for weak measurement of BEC spin quantum as claimed in claim 1, wherein in step S1, the cold atom in BEC state is Rb87An atom, the cold atomic energy level transition of said BEC state being | F ═ 1, mF＝-1>→|F＝1，mF＝0>；
The vacuum equipment is a glass vacuum cavity; the cold atoms of the BEC state are prepared by the microwaves
After the atoms are in the superposed state, the microwave is closed through the horn-shaped microwave waveguide;
the preparation conditions of the BEC state cold atoms are as follows:
the temperature of the cold atoms of the BEC state is 75 nk;
the purity of the cold atoms in the BEC state is more than 90%;
the number of atoms of the cold atoms of the BEC state is 1.5 x 105；
The critical temperature of the cold atoms of the BEC state satisfies the following first calculation formula:
wherein, TCIs the critical temperature, n is the particle density, m is the mass of each boson,
the reduced Planck constant (Dirac constant), pi is 3.1415926, kBZeta is a Riemann zeta function, and is a Boltzmann constant, and is 2.6124 taken as Zeta (3/2).
4. The method of claim 1, wherein in step S2, the anti-helmholtz coil generates a gradient magnetic field in z direction, and the atoms in the superposition state generate two first clusters of atoms by using a Stern-Gerlach apparatus; the two first radicals are
And
two groups of atoms of (a); the microwave is turned off after the first radical is obtained.
5. The method according to claim 1, wherein in step S3, the spin state of the first two clusters is transformed from | S > to | S' > and the quantization axis of the pseudo spin is rotated by 90 °.
6. The method for weak measurement of BEC spin quantum as claimed in claim 1, wherein in step S4, the anti-Helmholtz coil has a total of 60 coils in one direction, wherein each 20 coils is divided into three groups;
the number of the anti-Helmholtz coils is 2, the inner diameter of each anti-Helmholtz coil is 60mm, the outer diameter of each anti-Helmholtz coil is 140mm, and the distance between the two anti-Helmholtz coils is 83 mm;
the current of 200A can be passed through each group of coils, the longitudinal magnetic field gradient of 2.19Gs/cm/A is generated by each group of coils, and the transverse magnetic field gradient of 1.095Gs/cm/A is generated by each group of coils.
7. The method for weak measurement of BEC spin quantum as claimed in claim 1, wherein in the step S5, the CCD/CMOS target surface size of the CDD camera is 1/3 inches, and each pixel of the CDD camera is 3.75 μm;
the process of obtaining spin values by centroid calculation of the target radical comprises:
s501: measuring a density distribution of BEC cold radicals from an image obtained by the CDD camera;
s502: fitting a centroid position according to the coordinates and gray values of each position of the pixels in the image;
s503: calculating and obtaining the spin value of the target atomic group by using a second calculation formula according to the electric field intensity and the centroid position;
the spin state to be measured of the cold atom in the BEC state is psi, and psi can be expressed as: Σ ═ Σici|Ψi>Wherein | Ψi>Is a spin operator
The eigenstate of (a);
the spin operator
And said eigenstate | Ψi>In a relationship of
The spin operator is used when the cold atom of the BEC state is in a psi state
The expectation of (c) may be expressed as:
when sigmai|ci|2·si.When the measurement is impossible, the spin operator is measured by using the pointer state
The expected value of (d);
the pointer state is a momentum wave function of the cold atoms of the BEC state;
the initial momentum state of the cold atoms of the BEC state is
In the process of BEC spin quantum weak measurement, the Hamiltonian quantity is
In the step S503, the spin operator is subjected to
Converting the measurement of the expected value of (a) to a measurement of the waveform centroid position offset;
in the step S503, the second calculation formula is adopted for the measurement of the waveform centroid position shift;
the second calculation formula is:
therein, sigmai|ciφ(p-p0-gsi)|2Is a momentum probability distribution; g is the coupling strength or interaction strength; siIs composed of
The eigenvalues of (a); p is a radical ofiMomentum distribution as a function of wave; integral sum ofi|ciφ(p-p0-gsi)|2dp is the wave function probability distribution.
8. An apparatus for BEC spin quantum infinitesimal measurement as used in any one of claims 1-7, comprising a microwave horn, cold atoms in the BEC state, an anti-helmholtz coil, a CCD camera;
the microwave horn is used for generating a microwave electric field;
the cold atoms in the BEC state are placed in a vacuum device and used for observing results after different spin states;
the anti-Helmholtz coil generates a gradient magnetic field, and a Stern-Gerlach device is utilized to measure the cold atoms in the BEC state;
the CCD camera is used for selecting the cold atoms in the BEC state to carry out absorption imaging.
9. An apparatus for BEC spin quantum interferometry according to claim 8, wherein said microwave horn, said BEC-state cold atoms, said anti-helmholtz coil, and said CCD camera are all in an experimental coordinate system;
the experimental coordinate system comprises an x axis, a y axis and a z axis;
the three directions of the x axis, the y axis and the z axis are mutually vertical;
the transmitting direction of the microwave is incident at an angle of 45 degrees with the x axis and the y axis in the experimental coordinate system.
10. The apparatus according to claim 8, wherein the container of cold atoms in the BEC state is a vacuum device, and the vacuum device is a glass vacuum chamber; the vacuum degree of the vacuum apparatus was 8.6 x 10 without opening the cold atoms of the BEC state-9pa, degree of vacuum of the vacuum apparatus in the case of opening the cold atoms of BEC state is 1.2 x 10-8pa。
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